NEWSLETTER No. 43

March 2002

EMS Agenda ................................................................................................. 2

Editorial ........................................................................................................ 3

Executive Committee Meeting Brussels ...................................................... 4

EMS News ..................................................................................................... 7

EMS-SIAM Conference .................................................................................. 8

Aniversary - Niels Henrik Abel ................................................................... 12

Interview - Sir John Kingman...................................................................... 14

Interview - Sergey P. Novikov ..................................................................... 16

Union of Czech Mathematicians and Physicists .......................................... 20

Mathematicians Careers ............................................................................ 22

Forthcoming Conferences ............................................................................ 29

Recent Books ............................................................................................... 36

Designed and printed by Armstrong Press LimitedCrosshouse Road, Southampton, Hampshire SO14 5GZ, UK

telephone: (+44) 23 8033 3132 fax: (+44) 23 8033 3134Published by European Mathematical Society

ISSN 1027 - 488X

The views expressed in this Newsletter are those of the authors and do not necessarilyrepresent those of the EMS or the Editorial team.

NOTICE FOR MATHEMATICAL SOCIETIESLabels for the next issue will be prepared during the second half of May 2002.Please send your updated lists before then to Ms Tuulikki Mäkeläinen, Department ofMathematics, P.O. Box 4, FIN-00014 University of Helsinki, Finland; e-mail:makelain@cc.helsinki.fi

INSTITUTIONAL SUBSCRIPTIONS FOR THE EMS NEWSLETTERInstitutes and libraries can order the EMS Newsletter by mail from the EMS Secretariat,Department of Mathematics, P. O. Box 4, FI-00014 University of Helsinki, Finland, or by e-mail: (makelain@cc.helsinki.fi). Please include the name and full address (with postal code),telephone and fax number (with country code) and e-mail address. The annual subscription fee(including mailing) is 65 euros; an invoice will be sent with a sample copy of the Newsletter.

EDITOR-IN-CHIEFROBIN WILSONDepartment of Pure MathematicsThe Open UniversityMilton Keynes MK7 6AA, UKe-mail: r.j.wilson@open.ac.uk

ASSOCIATE EDITORSSTEEN MARKVORSENDepartment of Mathematics Technical University of DenmarkBuilding 303DK-2800 Kgs. Lyngby, Denmarke-mail: s.markvorsen@mat.dtu.dkKRZYSZTOF CIESIELSKIMathematics Institute Jagiellonian UniversityReymonta 4 30-059 Kraków, Polande-mail: ciesiels@im.uj.edu.plKATHLEEN QUINNThe Open University [address as above]e-mail: k.a.s.quinn@open.ac.uk

SPECIALIST EDITORSINTERVIEWSSteen Markvorsen [address as above]SOCIETIESKrzysztof Ciesielski [address as above]EDUCATIONTony GardinerUniversity of BirminghamBirmingham B15 2TT, UKe-mail: a.d.gardiner@bham.ac.ukMATHEMATICAL PROBLEMSPaul JaintaWerkvolkstr. 10D-91126 Schwabach, Germanye-mail: PaulJainta@aol.com ANNIVERSARIESJune Barrow-Green and Jeremy GrayOpen University [address as above]e-mail: j.e.barrow-green@open.ac.ukand j.j.gray@open.ac.uk andCONFERENCESKathleen Quinn [address as above]RECENT BOOKSIvan Netuka and Vladimir Sou³ekMathematical InstituteCharles UniversitySokolovská 8318600 Prague, Czech Republice-mail: netuka@karlin.mff.cuni.czand soucek@karlin.mff.cuni.czADVERTISING OFFICERVivette GiraultLaboratoire dAnalyse NumériqueBoite Courrier 187, Université Pierre et Marie Curie, 4 Place Jussieu75252 Paris Cedex 05, Francee-mail: girault@ann.jussieu.frOPEN UNIVERSITY PRODUCTION TEAMLiz Scarna, Kathleen Quinn

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CONTENTS

EMS March 2002

EDITORIALTEAM EUROPEAN MATHEMATICAL SOCIETY

EXECUTIVE COMMITTEEPRESIDENT (19992002)Prof. ROLF JELTSCHSeminar for Applied MathematicsETH, CH-8092 Zürich, Switzerlande-mail: jeltsch@sam.math.ethz.chVICE-PRESIDENTSProf. LUC LEMAIRE (19992002)Department of Mathematics Université Libre de BruxellesC.P. 218 Campus PlaineBld du TriompheB-1050 Bruxelles, Belgiume-mail: llemaire@ulb.ac.beProf. BODIL BRANNER (20012004)Department of MathematicsTechnical University of DenmarkBuilding 303DK-2800 Kgs. Lyngby, Denmarke-mail: bbranner@mat.dtu.dkSECRETARY (19992002)Prof. DAVID BRANNANDepartment of Pure Mathematics The Open UniversityWalton HallMilton Keynes MK7 6AA, UKe-mail: d.a.brannan@open.ac.ukTREASURER (19992002)Prof. OLLI MARTIODepartment of MathematicsP.O. Box 4FIN-00014 University of HelsinkiFinlande-mail: olli.martio@helsinki.fi ORDINARY MEMBERSProf. VICTOR BUCHSTABER (20012004)Department of Mathematics and MechanicsMoscow State University119899 Moscow, Russiae-mail: buchstab@mendeleevo.ru Prof. DOINA CIORANESCU (19992002)Laboratoire dAnalyse NumériqueUniversité Paris VI4 Place Jussieu75252 Paris Cedex 05, Francee-mail: cioran@ann.jussieu.frProf. RENZO PICCININI (19992002)Dipartimento di Matematica e ApplicazioniUniversità di Milano-BicoccaVia Bicocca degli Arcimboldi, 820126 Milano, Italye-mail: renzo@matapp.unimib.itProf. MARTA SANZ-SOLÉ (2001-2004)Facultat de MatematiquesUniversitat de BarcelonaGran Via 585E-08007 Barcelona, Spaine-mail: sanz@cerber.mat.ub.esProf. MINA TEICHER (20012004)Department of Mathematics and Computer ScienceBar-Ilan UniversityRamat-Gan 52900, Israele-mail: teicher@macs.biu.ac.il EMS SECRETARIATMs. T. MÄKELÄINENDepartment of MathematicsP.O. Box 4FIN-00014 University of HelsinkiFinlandtel: (+358)-9-1912-2883fax: (+358)-9-1912-3213telex: 124690e-mail: makelain@cc.helsinki.fiwebsite: http://www.emis.de

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EMS NEWS

EMS March 2002

200219-21 AprilEMS brainstorming meeting at Berlingen (Switzerland)

22-26 April EMS Lectures by Prof. Gianni Dal Maso (SISSA, Trieste, Italy): Neumann problems in domains with cracks and applications to fracture mechanics Max Planck Institute for Mathematics in the Sciences, Leipzig (Germany).Contact: Prof. Stefan Müller, e-mail: sm@mis.mpg.de

13-17 MayEMS Lectures by Prof. Gianni Dal Maso (SISSA, Trieste, Italy): Neumann problems in domains with cracks and applications to fracture mechanics Laboratoire dAnalyse Numérique, Université Paris VI.Contact: Prof. François Murat, e-mail: murat@ann.jussieu.fr

15 MayDeadline for submission of material for the June issue of the EMS NewsletterContact: Robin Wilson, e-mail: r.j.wilson@open.ac.uk

19-31 MayEMS Summer School in Craiova (Romania):Mathematical and numerical methods in computational quantum chemistryContact: Yvon Maday, e-mail: maday@ann.jussieu.fr

31 May Executive Committee meeting in Oslo (Norway).

1-2 June EMS Council Meeting, Oslo.

3-8 JuneAbel Bicentennial Conference, Oslo.

21-26 June EURESCO Conference: Discrete Painlevé Equations and the Solvability of Difference Equationsin Giens, near Toulon (France)webpage: http://www.esf.org/euresco/02/

1-5 July Congrès de Mathématiques Appliquées à la mémoire de Jacques-Louis LionsCollège de France, Paris (France)e-mail: congres.jllions@ann.jussieu.fr webpage: http://acm.emath.fr/congres-jllions

15 AugustDeadline for submission of material for the September issue of the EMS NewsletterContact: Robin Wilson, e-mail: r.j.wilson@open.ac.uk

28-29 SeptemberExecutive Committee meeting in Stockholm, at the invitation of the SwedishMathematical Society

31 DecemberDeadline for bids for the Fifth European Mathematical Congress, 5ecm, in 2008Contact: EMS Secretariat, e-mail: makelain@cc.helsinki.fiDeadline for Raising Public Awareness Article CompetitionContact: Vagn Lundsgaard Hansen, e-mail: V.L.Hansen@mat.dtu.dk

200310-13 FebruaryEMS-SMAI-SMF Meeting in Nice (France).Mathématiques Appliquées - Applications des Mathématiques (Applied Mathematics -Applications of Mathematics)Contacts: Doina Cioranescu, e-mail: cioran@ann.jussieu.frand Mireille Martin-Deschamps, e-mail: mmd@math.uvsq.frwebpage: http://acm.emath.fr/amam/

1 MarchDeadline for proposals for 2004 EMS Lectures Contact: David Brannan, e-mail: d.a.brannan@open.ac.uk

EMS AgendaEMS Committee

French mathematicians are grouped intotwo learned societies, the SociétéMathématique de France (SMF) and theSociété des Mathématiques Appliquées etIndustrielles (SMAI).

The SMF (http://smf.emath.fr/) is a non-profit organisation, founded in 1872,whose purpose is to defend and promotemathematics and mathematicians. Today,its membership reaches 2000, with most ofits members being in academics, but alsoincluding institutional members such aslibraries and mathematics departments.Its headquarters are located within theInstitut Henri Poincaré in Paris, and thereis also an Annex in Marseille on theCampus of the University in Luminy,which deals with the storage and diffusionof the SMFs publications.

The activities of the SMF include:- publication of professional books and

journals- management of the CIRM (Centre

International de RencontresMathématiques), located on the Luminycampus

- lobbying on behalf of mathematics withpolitical authorities

- animation and reflection within the com-munity concerning teaching andresearch in mathematics

- popularisation of Mathematics forexample, via the dAlembert prizeawarded every other year.

The SMAI (http://smai.emath.fr/) was found-ed in the early 1980s, when a large portionof the applied mathematics community feltthe need to have specific representation.Since then, the SMAIs membership hasrisen to close to 1400, including institu-tional members, such as the research cen-tres of some private or semi-public corpo-rations, as well as the applied mathematics

departments of several of the FrenchGrandes Ecoles and universities. Asidefrom its lobbying on behalf of the appliedmathematics community, the SMAI isinvolved in the publication of journals(ESAIM series with EPS SciencePublishing) and a lecture notes series(Mathématiques et Applications withSpringer), and in the organisation of manymeetings, including the yearly CongrèsdAnalyse Numérique and the SMAI Congres(every 4 years). It has four special interestgroups (concerned with numerical analysisin industry; statistical methods and appliedprobability theory; optimisation and oper-ational research; function approximation)which hold their own yearly meetings.Relations with other scientific societiessuch as the SMF, the Societé Française deStatistics and the Société Française dePhysique are well developed. The SMAIwas a founding member of theInternational Council for Industrial andApplied Mathematics, and organised thefirst ICIAM Congress in Paris in 1987.

The existence of the two societies doesnot split the mathematical community, asthere are many joint members and the twosocieties have several joint projects andactivities.

Both societies are involved in interna-tional collaboration, particularly at theEuropean level, and they took part in theWorld Mathematical Year 2000 project,from its onset. On this occasion theylaunched the ACM

The SMAI and the SMF were bothinstrumental in the creation of the EMS, ofwhich they are both founding members.So, when the question was raised of how toincrease the role of applied mathematics inthe EMS, they acted jointly and took partin the Berlingen meeting in May 2001.

In the recent past, mathematicians havebecome aware of the broad needs of math-ematics in other sciences and in technolo-gy, and have responded positively. Asapplications have become more sophisti-cated and complex, they have required theinput of many branches of mathematics,some until recently considered as very fun-damental, thereby making the distinctionsbetween pure and applied mathematicsless sharp.

AMAM 2003After the Berlingen meeting, the EMS pro-posed the organisation of a conference onthis subject. They suggested that the con-ference be organised jointly by the SMFand the SMAI, be held in Nice, and becalled Applied Mathematics and Applications ofMathematics (AMAM 2003). It will be heldat the Palais des Congrès in Nice from 10to 15 February 2003.

The co-presidents of AMAM 2003 areRolf Jeltsch, Michel Théra and MichelWaldschmidt. The Scientific Committee isco-chaired by Pierre Louis Lions (France)and Sergey Novikov (Russia), and its mem-bers are Lucien Birgé (France), Jean-Michel Coron (France), Marie-FrançoiseCoste-Roy (France), Alain Damlamian(France), Nicole El Karoui (France),Antonio Fasano (Italy), Olivier Faugeras(France), Andras Frank (Hungary),François Golse (France), Michael Gromov(France), Eugene Ya. Khruslov (Ukraine),Peter Alexander Markowich (Austria),Michel Merle (France), Jean-FrançoisMestre (France), Etienne Pardoux(France), Olivier Pironneau (France),Frédéric Poupaud (France), Dirk Roose(Belgium), Zeev Schuss (Israel), J.TrevorStuart (UK), Eitan Tadmor (Israel andUSA) and Vladimir V. Vasin (Russia). TheOrganising Committee is co-chaired byDoina Cioranescu and Mireille Martin-Deschamps, and also contains JacquesBlum, Denise Chenais and Charles Waltefrom the University .of Nice.

The conference is structured according tothe following list of topics:1. Applications of number theory, includ-

ing cryptography and coding2. Control theory, optimisation, opera-

tional research and system theory3. Applications of mathematics in biology,

including genomics, medical imaging,models in immunology, modelling andsimulation of biological systems

4. Scientific computation, including abinitio computation and moleculardynamics

5. Meteorology and climate, includingglobal change

6. Financial engineering7. Signal and image processing8. Non-linear dynamics9. Other applications: probability and sta-

tistics, inverse problems, fluid dynam-ics and material sciences

There will be 12 plenary speakers, 30 mini-symposia, three round tables and twoposter sessions. The following have alreadyagreed to present a plenary lecture: AlfredM. Bruckstein (Israel), Robert S. Eisenberg(USA), Roland Glowinski (USA), LeslieGreengard (USA), Eugenia Kalnay (USA),Roland Keunings (Belgium), DavidLevermore (USA), Pascal Massart (France),Marek Musiela (UK), René Schoof (Italy)and Enrique Zuazua (Spain). All EMS members are invited to partici-pate in AMAM 2003: why not propose aminisymposium or a poster?

For information and registration pleaserefer to our website: http://acm.emath.fr/amam/

Doina Cioranescu is Director of Research atCNRS, Laboratoire Jacques-Louis Lions,Université Pierre et Marie Curie, 175 rue duChevaleret, 75013 Paris, France.Mireille Martin-Deschamps is Professor at theLaboratoire de Mathématiques, Université deVersailles et Saint-Quentin, 45 avenue desEtats-Unis, 78035 Versailles Cedex, France.

EDITORIAL

EMS March 2002 3

EditorialEditorialand AMAM 2003 Announcement

Doina Cioranescu and Mireille Martin-Deschamps

Doina Cioranescu

Present: Rolf Jeltsch (President, in theChair), David Brannan, Bodil Branner,Victor Buchstaber, Doina Cioranescu, LucLemaire, Olli Martio, Marta Sanz-Solé,Mina Teicher. Apologies had been receivedfrom Renzo Piccinini.

In attendance by invitation: CarlesCasacuberta (Publications Officer), Robin

Wilson (Editor-in-Chief, Newsletter), DavidSalinger (Publicity Officer), Saul Abarbanel(Chair of the Applied MathematicsCommittee), Ari Laptev (Chair of the LocalOrganising Committee of 4ecm), ThomasHintermann (Managing Director of theEMS Publishing House), Sir JohnKingman (nominee for EMS President for2003-06), Helge Holden (nominee forEMS Secretary for 2003-06), and TuulikkiMäkeläinen (Helsinki Secretariat).

The President thanked the UniversitéLibre de Bruxelles and the BelgianMathematical Society for their invitationand generous hospitality, and welcomedall participants.

Officers ReportsThe President reported on the compositionof the Scientific Committee of amam03, theBy-Laws of the European MathematicalFoundation, MATHDI, the appointmentof Manuel Castellet as Chair of ERCOM,extension of the time for the EMS-RPAcompetition, and on the EMS SummerSchools. He reported that at the EMS-SIAM conference in Berlin there had been420 participants from 42 countries, includ-ing 36 European countries and all EU andAssociated States.

The Zentralblatt Consultative Committeemeeting on 6 November 2001 inHeidelberg had been business-like androutine. The EMS is now trying to furtherthe drive to make ZentralblattMATH a trulyEuropean endeavour, starting with a brain-storming weekend in Berlingen on 19-21April 2002.

Luc Lemaire and Rolf Jeltsch attended

the following two events in Brussels: theConference of the Belgian Presidency ofthe European Unions Research CouncilEvent (creation of the European ResearchArea) and a conference on International bestpractices in evaluation of research in publicinstitutes and universities. On both occasionsthey were able to talk briefly to the

Commissioner Ph. Busquin. The EMS hadpointed out that no mathematicians wereon his Scientific Advisory Board of 45 per-sons.

Rolf Jeltsch had attended an informalmeeting on digitising (in a searchable way)mathematical literature during the JointMathematics Meeting of the AMS, MAAand SIAM in San Diego.

The Treasurer reported that the finan-cial state of the EMS was sound. TheFinancial Statements for the year 2001were accepted and signed by the ExecutiveCommittee members; it was noted that theSociety currently has an Investment Fundof 70K euro, in shares and investmentfunds, together with some cash in hand. Abudget proposal for 2003 and 2004 wasagreed for presentation to the Council inOslo. There was some discussion of presi-dential expenses, and the need not to limitthe choice of President to people with theirown sources of funding.

The Publicity Officer proposed that theEMS prepare a letter to go in corporatesocieties mailings to their members, andthis was agreed; electronic distributioncould be considered. The EMS wouldshare a booth with Zentralblatt at ICM-2002in Beijing, would have a booth at the AbelConference in Oslo until the Tuesday, andwould have a booth at amam03 in Nice. Itwas agreed that contact should be madewith member societies whose number ofEMS members has not increased recently.A new venture, the AlphaGalileo Project, isseeking to improve the communication ofEuropean research to the worlds media(http://www.alphagalileo.org); from late

spring 2002 it will include mathematics.AlphaGalileo is a collaboration betweenFinland, France, Germany, Greece,Portugal and the UK, with support fromthe ESF and other European bodies. It wasagreed to make positive contact with itsorganisers.

On the Secretarys suggestion, DavidSalinger was elected Publicity Officer for afurther term of 2003-05.

The Helsinki Secretariat reported onsome membership matters that wouldhopefully be ready for Council, and therewas a brief discussion of the need to regis-ter mathematical societies in Russia at themoment. At the request of certain membersocieties in need, a reduction in their EMSdues for specific years was agreed.

Scientific MeetingsMina Teicher reported on the SummerSchools in 2002 in Eilat and Craiova.Applications to the EU for summer schoolsin Spain, Porto and CIME had been sub-mitted for future years. There was a viewthat the EMS should select subjects forsummer schools and then ask societies oractive people to organise the schools.

A call had been circulated for sugges-tions for the 2003 EMS Lecturer, preferablyin a more pure field. Professor Gianni DalMaso of SISSA, Trieste, was the EMSLecturer for 2002, and would speak at theUniversity of Paris VI and the Max PlanckInstitute in Leipzig.

The Diderot Mathematical ForumDMF5 on Mathematics andTelecommunication had taken place inLausanne, Eindhoven and Helsinki. Muchof the scientific programme had beenexcellent, and the video conferencing hadbeen successful. There was a discussion ofthe future of the Diderot MathematicalForums, and a feeling that the EMS shouldthink afresh about the DMF concept, inorder to maximise the value of Societyactivities.

Ari Laptev, President of the OrganisingCommittee of the 2004 European Congressof Mathematics in Stockholm, reported onthe progress made for the Congress. The4ecm has now a home page athttp://www.math.kth.se/~4ecm. LennartCarleson (Stockholm) will be Chair of theScientific Committee and Björn Engquist(Stockholm) its Vice-Chair; and other pos-sible members of the Committee were dis-cussed, including the need for balance inits composition. Only the Chair and Vice-Chair will be made public.

There was a stimulating discussion of theEMS Prizes, and several recommendationswill be put to Council: 1. Eligibility for an EMS Prize is open to

any European mathematician who hasnot reached his/her 35th birthday on 30

EMS NEWS

EMS March 20024

EMS Executive Committee Meeting EMS Executive Committee Meeting Brussels (Belgium), 9-10 February 2002

June of the year of the congress. In theevent of a possible candidate havinghad a broken career pattern, a corre-sponding increase in age will be accept-able at the discretion of the PrizeCommittee, up to a maximum of threeadditional years. By way of exampleonly, this provision is intended to coveritems such as military service, womenhaving children, etc.

2. A mathematician is defined to beEuropean in the context of EMS Prizesif they are of a European nationality ortheir normal place of work is withinEurope/substantial amount of theirmathematical work done in Europe.

3. The Prize Committee will endeavour toensure a fair balance of nominations, asregards the following criteria: specialitywithin mathematics, nationality, andgeographical base.

4. Following the identification of the Chairof the Prize Committee, their name,address and e-mail address will be pub-lished in the EMS Newsletter, togetherwith an invitation from the Chair to allmathematicians to send in suggestionswith reasons and one or two names ofpeople who could be contacted with fur-ther information on the nominee. Thecall should be published in theNewsletter, on EMIS, sent to societiesand mentioned on the Congress webpage.

5. The place of work in the rules isintended to include place of study.

6. Prizes are to be awarded for the scientif-ic merit of the persons work.

7. The Chair of the Prize Committee willsuggest the members of the PrizeCommittee for approval by the EMSExecutive Committee. Their identitieswill not be made public until after thePrizes are awarded.

The Prize Committee for the Felix KleinPrize consists of three persons from theEMS, two from the KaiserslauternInstitute, and one from ECMI.

A call for bids to hold the 2008 ECMappeared in the December Newsletter andwill be repeated.

There will be a conference, amam03, inNice on 25-27 June 2003 with the titleApplied Mathematics - Applications ofMathematics, sponsored jointly with SMAIand SMF. It will be chaired by Rolf Jeltsch,Michel Thera and Michel Waldschmidt.The Scientific Committee Co-Chairs arePierre-Louis Lions (Université Paris-Dauphine) and Sergei P. Novikov(University of Maryland and Moscow), andthe Scientific Committee Coordinator isAlain Damlamian (Université Paris 12).The Local Organising Committee consistsof: Doina Cioranescu (Université Paris VI)(Chair), Mireille Martin-Deschamps(Université de Versailles) (Chair), JacquesBlum, Denise Chenais and Charles Walter(Université de Nice Sophia-Antipolis).There will be a discounted conference feefor members of the EMS, SMF and SMAI.The Congress web address is:http://www.acm.emath.fr/amam.

The EC agreed to give moral support toa conference Janos Bolyai CommemoratingYear 2002 on 8-12 July 2002 in Cluj.

The next EMS Council meeting will be on1-2 June 2002, starting on Saturday 1 Juneat 10 a.m., in Auditorium 2 of GeorgSverdrups Hus, on the University of Oslocampus. The delegates representing indi-vidual members are: Giuseppe Anichini(1996-99-03), Vasile Berinde (2000-03),Giorgio Bolondi (1996-99-03), AlbertoConte (2000-03), Chris Dodson (2000-03),jean-Pierre Francoise (2000-03), SalvadorS. Gomis (2000-03), Laurent Guillopé(2000-03), Klaus Habetha (1996-99-03),Willi Jaeger (2000-03), Tapani Kuusalo(1996-99-03), Marina R. Marchisio (1998-2001-05), Vitali Milman (1998-2001-05),László Márki (1996-99-03), AndrzejPelczar (2000-03), Zéev Rudnick (2000-03), Gérard Tronel (2000-03), RobinWilson (2002-05), and Sebastià Xambó-Descamps (2002-05).

Committee Reports will be written, withpossibly a few minutes oral representationat the meeting, followed by a question andanswer session. Committee chairs will beinvited to attend. There will be a presenta-tion of 4ECM within the Council meeting.

The Executive Committees nomina-tions for the President (Sir John Kingman),Vice-President (Luc Lemaire), Secretary(Helge Holden) and Treasurer (OlliMartio) had been decided earlier, andthere was a discussion on nominations forthe other vacancies. There was also a stim-ulating discussion of essentially technicalchanges to the Statutes and By-Laws thatwould be proposed to Council by theExecutive Committee.

The President was arranging an ad hocmeeting Berlingen 2: Publishing, Meetings,Integrated Initiatives, on 19-21 April 2002.Among the topics would be ZentralblattMATH, Digitalisation and EMS Publishing.

Society CommitteesIt was agreed to publish the remits of thecommittees on EMIS, to have a Vice-Chairfor each Committee, terms of office for allcommittee members, and an ExecutiveCommittee member as a contact for eachCommittee. There will be a meeting of the

Chairs of Committees in Oslo on 2 June2002 from 2-4 p.m., chaired by RolfJeltsch.

Saul Abarbanel reported his wish for theApplied Mathematics Committee to meetannually. It was decided to reconsider therole and future of the Databases Committeein Berlingen. Manuel Castellet (2002-05)had succeeded Ole E. Barndorff-Nielsen(1998-2001) as Chair of ERCOM. MinaTeicher had become Acting Chair of theSummer Schools Committee during theabsence abroad of Renzo Piccinini (2000-03); it was decided to dissolve thisCommittee, and to discuss the question ofhow to organise summer schools in future(possibly via the planned MeetingsCommittee) in Berlingen in April. It was alsoagreed to discuss the future of thePublications Committee (Carles Casacuberta,1998-2001-02) in Berlingen. TheExecutive Committee reminded itself thatit had agreed previously to set up aMeetings Committee, to be initiallychaired by Luc Lemaire (2001-04)

The Education Committee had discussedwith EU a possible follow-up to theReference Levels Project for 16-year-olds,to cover the group up to 18-year-olds.

PublishingThe Board of Trustees of EuropeanMathematical Foundation (EMF) hadapproved the final version of the EMF By-Laws, which will now be registered with theChamber of Commerce in Zürich and withBerne, after which the EMF will become alegal body. The Statutes have been accept-ed by the Notary Public.

There was an important and lengthydiscussion of the business of the EMSPublishing House, which (for commercialreasons) will not be set out here. EMSphbusiness will be a topic for discussion at theOslo Council meeting. The Committeeagreed that, even simply by virtue of itsexistence, EMSph should encourage com-mercial publishers to do a better job formathematics.

It was agreed that all EC members whoknew of a good article for the EMSNewsletter should tell the Editor-in-Chiefabout it, and those not in English might betranslated subject of course to theauthors and publishers agreement. RobinWilson was appointed to a second term ofoffice (2002-04) as Newsletter Editor-in-Chief. It was again stressed that it wasimportant to have the Newsletter on EMIS,with a time lag of about six months beingappropriate.

The EC noted that Bernd Wegner,Editor-in-Chief of Zentralblatt, would reachhis 60th birthday on 18 February 2002. Itexpressed its unanimous congratulationsto him on this auspicious day, and wishedhim every happiness and many years tocome! His contribution to mathematics fora quarter-century as Editor-in-Chief ofZentralblatt had been outstanding, and thewhole mathematical community world-wide was greatly indebted to him.

The Publications Officer reported on anumber of volumes in various stages of thepreparation and production process.

EMS NEWS

EMS March 2002 5

Relations with Mathematical InstitutionsThere was a concerned discussion of thelack of adequate representation ofMathematics at the European ScienceFoundation (ESF), and it was agreed tomake strong representations to ESF on amore prominent position for mathemati-cians in ESFs PESC [Physical andEngineering Sciences StandingCommittee] and its working groups.

Rolf Jeltsch will represent the EMS atthe IMU General Assembly the EMS is anAffiliate Member of the IMU.

The EMS EC thanked the NorwegianAcademy of Sciences and Letters for creat-ing the Abel Prize for Mathematics, recog-nising it as a major event for mathematics.There are no restrictions on the subjectarea or age of prize-winners, and the selec-tion process will be very open. There willbe an Abel Prize Committee as well as aScientific Advisory Panel working to sup-port the Prize Committee.

It was agreed to publish a notice for theJ.-L. Lions Commemorating Conference in Julyin the EMS Newsletter.

Any Other BusinessThe EC had a stimulating and stimulateddiscussion of the Bologna Declaration. Onthe one hand it was agreed that the long-term autonomy of universities was impor-tant; on the other hand, that universitiescould not ignore that governments gener-ally supply most university fundingthroughout Europe.

It was agreed to draft a policy statementon the Bologna Declaration, which shouldbe discussed at Council in Oslo this

should be phrased in terms of the underly-ing principles to be supported by the EMS,rather than get involved in details thatwould vary from country to country.

Future EC/Council MeetingsThere will be an EC Meeting in Oslo on 31May 2002, to finalise preparations for theCouncil meeting starting the followingday. The meeting will be preceded by ameeting of the EMF Board of Trustees.

There will be a Council Meeting in Osloon 1-2 June 2002, in Auditorium 2, inGeorg Sverdrups Hus. This building is thenew University Library, located on theOslo University Campus. The meeting will

be followed by a meeting of the EMS Chairsof Committees.

At the invitation of the SwedishMathematical Society, an EC meeting willbe held on 28-29 September 2002 inStockholm. The Local OrganisingCommittee of amam2003 have invited theEC to meet in Nice on 9-10 February 2003.

And finally The EC participants expressed their heart-felt thanks to Luc Lemaire and hisUniversité Libre de Bruxelles and BelgianMathematical Society colleagues for a well-run meeting in a congenial atmosphere.

David A. Brannan

EMS NEWS

EMS March 20026

The EMS Council meets every secondyear. The next meeting will be held inOslo, Norway, on 1-2 June 2002, beforethe Abel Bicentennial Meeting in Oslowhich begins on 3 June. The first sessionof the Council meeting will start at 10 a.m.on 1 June, and will run all day with abreak for lunch. The second session willprobably start at 9 or 10 a.m. on 2 June,and may last most or all of the day with abreak for lunch, depending on the volumeand complexity of the business on theagenda.

Membership of the EMS ExecutiveCommitteeThe Council is responsible for electing thePresident, Vice-Presidents, Secretary,Treasurer and other members of theExecutive Committee. The present mem-bership of the Executive Committee,together with their individual terms ofoffice, is as follows.

PresidentProfessor Rolf Jeltsch (1999-2002)

Vice-PresidentsProfessor Luc Lemaire (1999-2002)

Professor Bodil Branner (2001-04)Secretary

Professor David Brannan (1999-2002)Treasurer

Professor Olli Martio (1999-2002)Members

Professor Victor Buchstaber (2001-04)Professor Doina Cioranescu (1999-

2002)Professor Renzo Piccinini (1999-2002)

Professor Marta Sanz-Solé (2001-04)Professor Mina Teicher (2001-04)

The President may serve only one term ofoffice, so Rolf Jeltsch cannot be re-electedas President. David Brannan and RenzoPiccinini have indicated that they do notwish to be re-elected. The ExecutiveCommittee proposes the names of SirJohn Kingman (Cambridge) for Presidentand Helge Holden (Trondheim) forSecretary

Under Article 7 of the Statutes, mem-

bers of the Executive Committee shall beelected for a period of 4 years. Committeemembers may be re-elected, provided thatconsecutive service shall not exceed 8years. No current member has served onthe Executive Committee for 8 years, soall existing Committee members are inprinciple available for re-election.

The Council may, at its meeting inOslo, add to the nominations receivedand set up a Nominations Committee, dis-joint from the Executive Committee, toconsider all candidates. After hearing thereport by the Chair of the NominationsCommittee (if one has been set up), theCouncil will proceed to the elections tothe Executive Committee posts.

If a nomination comes from the floorduring the Council meeting, there mustbe a written declaration of the willingnessof the person to serve, or his/her oralstatement must be secured by the chair ofthe Nominating Committee (if there issuch) or by the President. It is recom-mended that a statement of policy of thecandidates nominated from the floorshould be available.

Accommodation arrangementsDelegates to the Council meeting, who areplanning to attend the Abel CentennialMeeting, are advised that their accommo-dation arrangements should be madethrough the normal Abel CentennialMeeting organisation arrangements. Fordelegates to the Council who are notattending the Abel Centennial Meeting,an address for accommodation arrange-ments will be provided later.

Secretariat: Ms. Tuulikki MäkeläinenDepartment of Mathematics P. O. Box 4 FIN-00014 University of Helsinki Finland e-mail: makelain@cc.helsinki.fi

David BrannanSecretary of the EMSe-mail: d.a.brannan@open.ac.uk

Meeting of the EMS CouncilMeeting of the EMS CouncilOslo: 1-2 June 2002

From a mathematical point of view, thetopic chosen, Mathematics andTelecommunications: problems connected withcell phones, allowed the presentation of avery wide variety of mathematicalapproaches: from probability theory toharmonic analysis and algebra, severalareas of mathematics play, and will contin-ue to play an important role in the devel-opment of the subject. It is patent though,especially from what one heard during theForum, that some of the mathematicaltools needed are yet to be developed (cer-tainly in the stochastics area and in alge-braic coding, but somewhat more surpris-ingly in more mature areas of mathematicssuch as one-dimensional harmonic analy-sis), and that communications problemsthus offer a very attractive area for mathe-maticians.

The organisers were Paul Urbach(Philips Research Center Eindhoven),Olavi Nevanlinna (Helsinki University ofTechnology) and Gérard Ben Arous (ÉcolePolytechnique Fédérale de Lausanne).

The speakers were:For the lectures shared through the videolink:

(from Helsinki) Yrjo Neuvo (Helsinki):Mathematics for mobile communications,

(from Eindhoven) Joachim Hagenauer(Technische Universität München):Information and coding theory for mobilephones

(from Lausanne) R. Urbanke (EPFL,Lausanne): Low density parity check codes

In the Helsinki Workshop:Samuli Aalto (Helsinki University ofTechnology): Teletraffic analysis of multicastnetworks

Kaisa Nyberg (Nokia Research Center):Cryptography in UMTS

Ioan Tabus (Tampere University ofTechnology): On the use of the Hadamardtransform for index assignment over channelswith memory

Savo G. Glisic (University of Oulu):Modelling and analysis of code acquisitionprocess by using signal flow graph theory

Jyrki Lahtonen (University of Turku):Algebraic geometry in error correcting codes

Jyri Hämäläinen (Nokia Networks): TXdiversity feedback modes as a function of FB bits

Tapani Ristaniemi (University ofJyväskylä): Independent component analysisand CDMA

Pirkko Kuusela (Helsinki University ofTechnology): Internet congestion control delaydifferential equation models

Olav Tirkkonen (Nokia ResearchCenter): Clifford algebras and space time codes

Ilkka Norros (VTT InformationTechnology): Internet traffic as a stochasticprocess

In the Eindhoven Workshop :C.P.M. (Stan) Baggen (Philips Research,Eindhoven): Coding for informed decoders

Marc Moonen (Katholieke UniversiteitLeuven): Signal processing and mathematicalmodeling challenges in ADSL/VDSL high-speedtelephone line modems

Jean-Paul M.G. Linnartz (PhilipsResearch, Eindhoven): A mathematicalframework for resource management in wirelessnetworks

Philippe Godlewski (ENST, Paris):Models, achievable performance and capacitiesin cellular mobile networks

Richard J. Boucherie (University ofTwente, Enschede): Mobility and channelborrowing in mobile communications networks

Frans M.J. Willems (EindhovenUniversity of Technology): Embedding infor-mation in data-streams

Joergen Bach Andersen (AalborgUniversity): Electromagnetics and wirelesscommunications

Alle-Jan van der Veen (University ofTechnology Delft): Use of factor analysisanalysis in array signal processing

A.J.E.M. (Guido) Janssen (PhilipsResearch, Eindhoven): Gabor systems andcommunication theory

Luc Vandendorpe (UniversitéCatholique de Louvain): Signal processingaspects in CDMA systems.

In the Lausanne Workshop:Emre Telatar (EPFL): Application of randommatrices in communications

Alice Guionnet (CNRS-École NormaleSupérieure de Lyon): Some mathematicalaspects of random matrix theory in communica-tions

Marina Monsurro (EPFL): Algebrico-geo-metric codes

Piyush Gupta (Bell Labs, Murray Hill,USA), The traffic-carrying capacity of ad hocwireless networks

François Baccelli (INRIA, ÉcoleNormale Supérieure): Stochastic networksand topical maps

Patrick Thiran (EPFL): Connectivity inad-hoc networks

Jean-Yves Le Boudec (EPFL): Networkcalculus

Hans-Andrea Loeliger (ETH Zürich):Graphical models and signal processing

Martin Hasler (EPFL): Communicationsusing chaos

Martin Vetterli (EPFL and UCB):Sampling signals with finite rate of innovation

PresentationsSome of the presentations are available onthe following web sites:

for Helsinki: www.math.hut.fi/diderot2001for Eindhoven: www.research.philips.com

/diderot2001

for Lausanne: mawww.epfl.ch/benarous/Recherche/diderot.html

Video-conferencing technology The three cities were connected to eachother using a star network, with externalcentre node located in the University ofOulu, Finland. Lausanne and Eindhovenwere connected to Oulu using 384 kbpsISDN lines. Helsinki was connected toOulu through Internet (over the 2.5 GbpsFUNET backbone network).

It was interesting to share presentationsbetween the sites, although this required arelatively long broadcasting time. Someexpected better technical quality in thevideolinks.

From HelsinkiThere were 50 registered participants(including the 11 invited speakers). On thefirst conference day, there were approxi-mately 50 additional non-registered peo-ple attending the lectures given by Neuvo,Hagenauer, and Urbanke. The mainspeaker, Dr Yrjö Neuvo, reported that hehad been contacted afterwards by scientistsboth from Finland and from abroad andthat this feedback had been rewarding.

From EindhovenThere were approximately 85 registrationsfor the Eindhoven site: not everybodyshowed up on both days, but all lectureswere well attended. The emphasis inEindhoven was on signal processing andcoding theory, but there was also a lectureon electromagnetics for wireless communi-cations, by Bach Andersen. The level of thepresentations was well above average.Many who attended were very enthusiasticabout the quality of the lectures and haveasked the lectures to be placed on the web,which has been done (see above).

From LausanneAttendance was reasonably large (40). Theconference was opened from there by theEMS President, Rolf Jeltsch. Most partici-pants were obviously pleased by the qualityand diversity of the talks, as well as thedepth of the mathematical problemsunderlying the future progress of thisimportant area of engineering.

The forum was a true success on the sci-entific side, and an exciting event on thesocial side. Being jointly organised by peo-ple in communications (M. Hasler, M.Vetterli) and in mathematics (G. BenArous), its scientific programme could real-ly draw from both sides and show a verybroad spectrum of the possible interfacesof maths and telecoms. There were ses-sions on Stochastic methods in communi-cations, Networking, and Signals andSystems.

SuggestionIt may be a good idea for the future toorganise a poster session. This would giveyoung people the opportunity to presenttheir work, and would make the conferencemore lively. Of course, it would inevitablycause more work for the organisers.

Jean-Pierre Bourguignon

REPORT

EMS March 2002 7

Fifth Diderot Mathematical Forum

MAMATHEMATHEMATICS AND TELECOMMUNICATICS AND TELECOMMUNICATIONSTIONSEindhoven, Helsinki, and Lausanne

22-23 November 2001

The First EMS-SIAM Conference (webpage: http://www.zib.de/amcw01) tookplace on the attractive Science Campus ofthe Free University of Berlin. The localhost institution was the Zuse InstituteBerlin (ZIB), and the Co-Chairs were RolfJeltsch (ETH), Gil Strang (MIT) and PeterDeuflhard (ZIB); unfortunately, for sud-den health reasons, Gil Strang was unableto attend. More than 400 participantsfrom 42 countries (36 of them European)attended this event, with about 41% fromGermany and 8% from the US. Themajority of participants were quite young. The idea of the Conference was to bringtogether applied mathematics from bothsides of the Atlantic. As indicated by itstitle, the focus of the conference was onnew areas where applied mathematics is acoming main player, with a strong impe-tus from applications.

Scientific programmeAs is usual for such a large conference, thebackbone was the invited plenary talks,and of the invited speakers half camefrom Europe and half from the US (seebelow).

One of the most recent areas wheremathematics comes into play is genomics.Michael Waterman gave an excellentshort glimpse on algorithms for under-standing DNA sequences, where a lot ofdiscrete mathematics is involved. The lec-ture of Pietro Perona showed that we canalready do quite a bit using present math-ematics, but still have a long way to go tomake automatic visual recognition reallypossible.

Alfio Quarteroni demonstrated thatwhen classical computational fluid dynam-ics meets medical applications, new chal-lenges come up such as modelling thecardiovascular system for example, theinteraction of the walls of arteries with theblood flow.

The challenges in the simulation oftraffic throughout a whole country wereimpressively presented and discussed byKai Nagel. With the help of his methods,one can directly observe the bottlenecks.Unfortunately, the need for this kind ofsimulation became apparent immediatelyafter the Conference: He had, in fact,shown traffic flow simulations throughSwitzerland, with one or two pipes

through the Gotthard tunnel, the locationof a horrible accident shortly after.

The fact that new mathematics andsimulation tools are needed in materialsscience was demonstrated in two ratherdifferent ways by Jon Chapman andMichael Griebel. Jon Chapman derived athin-film model for superconductingmaterials by singular perturbation tech-niques.

Michael Griebel studied new nanotubeproperties of certain carbon materials, byapplying Hilberts space-filling curve tothe design of parallel adaptive multi-gridmethods. It is here that mathematiciansmay co-author materials patents.

Global models for the atmosphere cou-pled with ocean dynamics are known to betoo large for todays computers: AndrewMajda investigated new mathematicalpossibilities of modelling such coupledPDE systems. The derived smaller modelsbuild bridges to the whole large-scalemodels, which are currently beyond ourcomputability horizon.

Martin Grötschel demonstrated the dif-ficulties of designing optimal telecommu-nication networks. Even though integer

EMS NEWS

EMS March 20028

Applied Mathematics in our Changing WApplied Mathematics in our Changing WorldorldFirst EMS-SIAM Conference in Berlin, 2-6 September 2001

Peter Deuflhard and Rolf Jeltsch

The Computer Science Campus of the Free University ofBerlin with communication tent especially installed for the

conference (left, ZIB; right, Computer Science building)

programming is, in principle, well under-stood, the sheer size of the problems stillneeds a lot of mathematical intuition forthe invention of good theoretically-basedheuristics. The profit of such calculationsgoes into millions of euros.

Tom Hou studied microscale singulari-ties of three-dimensional vortex sheets,which may even be hard to detect in reallife. The mathematical difficulty stemsfrom Kelvin-Helmholtz instabilities thatmake the problem ill-posed.

For health reasons, Benoit Mandelbrotcould not be physically present in Berlinto deliver his lecture, but the organisersestablished a direct real-time connectionto IBM Yorktown Heights: this connectionmade it possible for Mandelbrot to deliverhis lecture, which put the Black-Scholesformula under strong dispute. Theimpression was as though he were directlyin the Berlin auditorium certainly aninteresting experience for all participants and the satellite connection was so goodthat there was a lively discussion at theend of the lecture.

A second backbone structure was theorganisation of 45 mini-symposia. Most ofthem lasted for two hours with four speak-ers presenting their results. The topics ofthe mini-symposia, which had been partlysolicited and all reviewed before, werechosen from the same areas as the plenarylectures. In addition, researchers present-

ed their latest results in 313 contributedpapers and 44 posters. These sessionswere arranged around the same topics asthe mini-symposia, and were scheduled sothat participants in the mini-symposiacould also attend the corresponding ses-sions of contributed papers. The idea wasthat international speakers coming fromdifferent schools of thought could fruitful-ly interact with the contributors.

Social programmeA communication tent had been especial-ly installed on the campus for theConference. It turned out to be the par-ticipants favourite meeting place over acup of coffee or tea or during lunchbreaks. Since all lectures were within walk-ing distance, most of the participantswalked together in small groups to thecommunication tent to continue their dis-cussions.

The evening before the conference, aget-together party took place in that tent,and after the Mandelbrot tele-lecturethere was a Barbecue Party which wasextremely well attended. The highlightsof the party were the open-air Klezmermusic from the balcony of the ZIB build-ing that could be heard down in the BBQarea and an indoor classical string quartet(Beethoven) in the greenhouse interior ofthe beautiful computer science building.

For pictures, see the web page:http://www.zib.de/amcw01/gallery/conf.htmlApart from these campus events, the ZIBstaff was extremely helpful. A cultural e-guide was prepared and some footloosetours were organised, which allowed par-ticipants and their companions to enjoyBerlin and its surroundings.

Round-table discussion: Applied Mathematics in EuropeThe round-table discussion was chaired byMartin Grötschel from ZIB. The panelistswere Rolf Jeltsch (ETH Zürich, Presidentof EMS), Tom Manteuffel (President ofSIAM), Joyce McLaughlin (RensselaerPolytechnical Institute), Hilary Ockendon(Oxford University and President of theEuropean Consortium for Mathematics inIndustry) and Alfio Quarteroni(Politecnico di Milano, Italy, and EPFLSwitzerland).

The discussion mainly focused on threepoints: what research should be done in

applied mathematics, trends and thefuture?

how should education at universitylevel cater for applied mathematics,inclusion in a general mathematicaleducation, and special curricula forapplied mathematics and also for com-putational science and engineering?

the structure of learned societies inmathematics and applied mathematicsin Europe.

Not only did the panellists give excellentcontributions, the discussion also benefit-ed greatly from the competence of theaudience which included many leadingapplied mathematicians in Europe, headof departments and presidents of soci-eties. The EMS sponsored a receptionafter the round-table where the discussioncontinued on a more informal level.

During the Conference, the EMS andSIAM discussed future joint conferencesthat could focus on more specialised top-ics. The EMS recognised that conferenceson the same level as the one in Berlinshould continue, probably on a biannualbasis, but maybe with varying partner soci-eties. The EMS Executive Committee hasalready decided to organise the next con-ference with the two French societies,Société Mathématique de France (SMF)and Société de MathématiquesAppliquées et Industrielles (SMAI). TheConference will be held in Nice, 10-13Feb 2003 and the topic will be AppliedMathematics Applications des Mathématiques(for details, see page 3). The main idea isto give young researchers in appliedmathematics an opportunity to get toknow new topics in applied mathematicsand applications of mathematics, and togive them a chance to network, exchangeviews and interact.

EMS NEWS

EMS March 2002 9

Co-Chairs Peter Deuflhard and RolfJeltsch with Erlinda Körnig, the engine

of the conference office.

Round table discussion with Martin Grötschel (Chair),Rolf Jeltsch, Tom Manteuffel, Joyce McLaughlin,

Hilary Ockendon and Alfio Quarteroni.

Queue during the BBQ party.

The 2002 EMS Lecturer will be ProfessorGianni Dal Maso (e-mail: dalmaso@sissa.it)of the International School for AdvancedStudies (SISSA) in Trieste, Italy.

He will visit two different locations inEurope to give the same series of lectureson Neumann problems in domains with cracksand applications to fracture mechanics to audi-ences in Leipzig and Paris (see detailsbelow), affording as many interested math-ematicians as possible the opportunity toattend, and to discuss the topics with him.

An abstract of his lecture series is as fol-lows: The first part of the course is devoted to thestudy of solutions to non-linear elliptic equa-tions in Ω K, where Ω is a two-dimensionalsmooth domain and K is a compact one-dimen-sional subset of Ω. The solutions are requiredto satisfy a homogeneous Neumann boundarycondition on K and a non-homogeneousDirichlet condition on δΩ. The main result isthe continuous dependence of the solution on K,with respect to the Hausdorff metric, providedthat the number of connected components of Kremains bounded. Classical examples show thatthe result is no longer true without this hypoth-esis.

Using this stability result, the second part ofthe course develops a rigorous mathematical for-mulation of a variational quasi-static model ofthe slow growth of brittle fractures, introducedby Francfort and Marigo. Starting from a dis-crete-time formulation, a more satisfactory con-tinuous-time formulation is obtained, with fulljustification of the convergence arguments.

EMS members and others interested inattending one of these series of lecturesare warmly welcomed to do so, and to talkinformally with Professor Dal Maso onrelated topics. However attendees arestrongly encouraged to contact the localorganisers of the series that they plan toattend in advance, so that the necessarypractical arrangements can be made (forexample, having a lecture room of suffi-cient size for everyone coming).

Local arrangementsLocation 1: Max Planck Institute forMathematics in the Sciences, LeipzigDates of the lectures: 22-26 April 2002Local contact: Prof. Stefan Müller, MaxPlanck Institute for Mathematics in theSciences, Inselstr. 22-26, D-04103Leipzig, Germany (e-mail: sm@mis.mpg.de) Location 2: Université Paris VI,Laboratoire dAnalyse Numérique Dates of the lectures: 13-17 May 2002 Local contact: Prof. François Murat,Université Paris VI, Laboratoire dAnalyseNumérique, Boite courrier 187, 75252PARIS Cedex 05, France (e-mail:murat@ann.jussieu.fr); telephone: +33-1-44274299; fax: +33-1-44277200

Brief biographyProfessor Dal Maso was born in Vicenza in1954; in 1955 his family moved to Trieste,where he had his basic education. He was

a student of the Scuola Normale of Pisafrom 1973 to 1977, and graduated inMathematics from the University of Pisa in1977, with Ennio De Giorgi as his advisor.He was then a graduate student of theScuola Normale di Pisa from 1978 to 1981,working with Professor De Giorgi on manyproblems connected with the theory ofgamma-convergence, that was developedin those years.

After serving as assistant professor ofMathematical Analysis in the Faculty ofEngineering of the University of Udinefrom 1982 to 1985, he moved to theInternational School for Advanced Studies(SISSA) in Trieste. He worked there asassociate professor of mathematical analy-sis from 1985 to 1987, and as full profes-sor of calculus of variations since 1987. Hewas awarded the Caccioppoli Prize in 1991and the Medaglia dei XL per laMatematica of the Accademia Nazionaledelle Scienze detta dei XL in 1996.

At SISSA he has developed his researchinterests on gamma-convergence,homogenisation theory, and free disconti-nuity problems, and has been the supervi-sor of 19 Ph.D. students working on thesesubjects. He currently serves as the headof the Sector of Functional Analysis andApplications of SISSA.

Research interestsProfessor Dal Maso started his researchwork in Pisa while Ennio De Giorgi wasdeveloping the new notion of gamma-con-vergence to deal in a systematic way withthe following kind of phenomena: thesolutions of variational problems depend-ing on a parameter may converge to thesolution of a limit problem, even if theintegrands of the functionals to be min-imised do not converge in any reasonablesense, or converge to a limit integrand thatis different from the integrand of the func-tional minimised by the limit of the solu-tions. Gamma-convergence is a very effi-cient tool to tackle these kinds of prob-lems.

In his work in Pisa and Udine he stud-ied several problems related to gamma-convergence. In particular he developed,with Giuseppe Buttazzo, several tech-niques for proving, under differenthypotheses, that the gamma-limits of inte-gral functionals are still integral function-als, and he studied, by gamma-conver-gence techniques, the asymptotic behav-iour of solutions to minimum problemswith strongly oscillating obstacles. Usingthe notion of capacity, he also gave a com-plete characterisation of the sequences ofobstacle problems whose variational limitis still an obstacle problem.

He later used these techniques to study,with Umberto Mosco, the asymptoticbehaviour of the solutions of Dirichletproblems for the Laplace equation in per-forated domains, and to determine thegeneral form of their variational limits, aswell as the fine properties of the solutions

of these limit problems. These resultshave been extended, with different collab-orators, to the case of other linear andnon-linear equations and systems.

At present his main research interestsare in free discontinuity problems. Theseare variational problems where the func-tional to be minimised depends on a func-tion and on its discontinuity set, whoseshape and location are not prescribed. Inmany cases the discontinuity set can beconsidered as the main unknown of theproblem. Examples are given by the min-imisation of the Mumford-Shah functionalin image segmentation, and by the mini-mum problems that appear in many varia-tional models for fracture mechanics,where the unknown crack is represented asthe discontinuity set of the displacementvector, and the functional to be minimisedis the sum of the elastic energy and of anintegral on the discontinuity set, whichrepresents the work done to produce thecrack.

Selected list of publicationsAn introduction to gamma-convergence, Birkhäuser,Boston, 1993.

Integral representation on BV(Ω) of Γ-limitsof variational integrals, Manuscripta Math. 30(1980), 387-416.

Asymptotic behaviour of minimum problemswith bilateral obstacles, Ann. Mat. Pura Appl. (4)129 (1981), 327-366.

Some necessary and sufficient conditions forthe convergence of sequences of unilateral con-vex sets. J. Funct. Anal. 62 (1985), 119-159.(with U. Mosco) Wiener criteria and energydecay for relaxed Dirichlet problems, Arch.Rational Mech. Anal. 95 (1986), 345-387.

(with G. Buttazzo) Shape optimization forDirichlet problems: relaxed formulation andoptimality conditions, Appl. Math. Optim. 23(1991), 17-49.

(with J. M. Morel and S. Solimini) A varia-tional method in image segmentation: existenceand approximation results, Acta Math. 168(1992), 89-151.

(with A. Garroni) New results on the asymp-totic behaviour of Dirichlet problems in perfo-rated domains. Math. Mod. Meth. Appl. Sci. 3(1994), 373-407.

(with L. Ambrosio and A. Coscia) Fine prop-erties of functions with bounded deformation,Arch. Rational Mech. Anal. 139 (1997), 201-238.

(with F. Murat) Asymptotic behaviour andcorrectors for Dirichlet problems in perforateddomains with homogeneous monotone opera-tors, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 24(1997), 239-290.

(with A. Braides) Non-local approximation ofthe Mumford-Shah functional, Calc. Var. PartialDifferential Equations 5 (1997), 293-322.

(with F. Murat, L. Orsina and A. Prignet)Renormalized solutions of elliptic equationswith general measure data, Ann. Scuola Norm.Sup. Pisa Cl. Sci. (4) 28 (1999), 741-808.

(with G. Alberti and G. Bouchitte) The cali-bration method for the Mumford-Shah func-tional, C. R. Acad. Sci. Paris Ser. I Math. 329(1999), 249-254.

(with R. Toader) A model for the quasi-stat-ic growth of brittle fractures: existence andapproximation results, Arch. Rational Mech.Anal., to appear.

EMS LecturEMS Lecturer 2002: Gianni Dal Masoer 2002: Gianni Dal Maso

EMS NEWS

EMS March 200210

EMS NEWS

EMS March 2002 11

Last year the European MathematicalSociety announced a competition toinspire the writing of articles with a math-ematical theme addressing a general audi-ence. The deadline for submissions wasoriginally set as 31 December 2001. Inresponse to comments, and to give moretime for suggestions of a wider range ofarticles, the Society has decided to acceptsubmissions in any European language and toextend the deadline for submission of articles to31 December 2002.

The advertisement of the competitionis repeated below, with the appropriatechanges incorporated. Vagn Lundsgaard HansenChair, Raising Public Awareness ofMathematics Committee (RPA)

Articles in many ways,math displays,

says,the EMS committee of RPA:A competition surely may,

inspire to the way,in which to pay,

as we say,attention to public awareness!

During World Mathematical Year 2000,many articles on mathematics addressing

ite) for the lecture series, the sites, and theorganisers of the schools will vary fromyear to year, to cover a wide range of thesubject.

The Society now invites proposals for at leastone Lecture Series for 2003. Proposals shouldcontain at least the topic (title and shortdescription), the name of the proposed lec-turer, the sites, the timing at each site, con-ditions for participants, and the name andaddress of the organiser submitting theproposal. Some preference will be given toapplications that involve the writing-up ofthe Lecture Notes into a volume suitablefor publication.

Please send proposals for series of EMSLectures in 2003, to:Professor D. A. Brannan, Faculty ofMathematics and Computing, The OpenUniversity, Walton Hall, Milton KeynesMK7 6AA, UK.Fax: +44 1908 652140; e-mail: d.a.bran-nan@open.ac.uk

Please send your proposals by 30 September2002 if possible; the Society would hope todecide on proposals within a month or so.

David A. Brannan, Secretary

a general audience were publishedthroughout the world, and many valuableideas for articles popularising mathematicswere generated. The Committee forRaising Public Awareness of Mathematicsof the European Mathematical Society(acronym RPA) believes that it is vital thatsuch articles be written. In order to inspirefuture articles with a mathematical themeand to collect valuable contributions, whichdeserve translation into many languages,the EMS wishes to encourage the submis-sions of articles on mathematics for a gen-eral audience, through a competition. TheEMS is convinced that such articles willcontribute to raising public awareness ofmathematics.

The RPA-committee of the EMS invitesmathematicians, or others, to submit man-uscripts for suitable articles on mathemat-ics.

To be considered, an article must bepublished, or be about to be published, ina daily newspaper, or some other generalmagazine, in the country of the author,thereby providing some evidence that thearticle does catch the interest of a generalaudience. Articles for the competitionshall be submitted both in the originallanguage (the published version) andpreferably also in an English translation.

Articles (translations) may, however, alsobe submitted in French, German, Italianor Spanish. The English (or alternativelanguage) version should be submittedboth on paper and electronically.

There will be prizes for the three bestarticles, of 200, 150 and 100 euros, and thewinning articles will be published in theEMS Newsletter. Other articles from thecompetition may also be published, ifspace permits. Furthermore, it is plannedto establish a web-site containing Englishversions of all articles from the competi-tion approved by the RPA Committee.

By submitting an article for the compe-tition, it is assumed that the author givespermission to translation of the articleinto other languages, and for possibleinclusion in a web-site. Translations intoother languages will be checked by per-sons appointed by relevant local mathe-matical societies and will be included onthe web-site.

Articles should be sent before 31December 2002 to the Chairman of the RPACommittee of the EMS: Professor Vagn Lundsgaard Hansen,Department of Mathematics, TechnicalUniversity of Denmark, Matematiktorvet,Building 303, DK-2800 Kongens Lyngby,Denmark. e-mail: V.L.Hansen@mat.dtu.dk

New deadline for Art ic le Competi t ionNew deadline for Art ic le Competi t ion

For some years the EuropeanMathematical Society has been running asuccessful series of EMS Lectures. In 2000G. Papanicolau gave a series of lectures onTime Reversed Acoustics at the University ofCrete (Heraklion) and on FinancialMathematics at ETH in Zürich, and the2001 EMS Lecturer, M. Vergne, spoke onConvex Polytopes at the University of Maltaand at the Universita Degli Studi Roma,Tor Vergata. The 2002 Lecturer is G. DalMaso (SISSA, Trieste), whose researchinterests include gamma-convergence,homogenisation theory, and free disconti-nuity problems

The EMS Lectures may be in pure orapplied mathematics, or may span bothareas; however, for 2003 the Society wouldprefer to appoint at least one lecturer inpure mathematics, in order to retain a rea-sonable balance. With this activity, theSociety aims to encourage European math-ematicians (especially young ones) to meetand study together current developmentsin mathematics and its applications. Thelectures should take place over several days(up to 5 days) in each of at least two loca-

tions, in order to give as many people aspossible the opportunity to attend. TheEMS will give some preference to lecturerswho visit institutions that might not nor-mally attract prominent lecturers or semi-nar speakers, and would prefer the geo-graphical locations of the lectures to be sig-nificantly distant from each other (forexample, North and South Europe, or Eastand West Europe), in order to maximisethe impact of the lectures.

The costs of participation should bekept low, and (if possible) grants should beavailable to people from countries thatcannot afford any financial support. TheEMS will guarantee its moral support tothe selected lecture series, and will pay forthe lecturers travel costs and for postersadvertising the lectures within theEuropean mathematical community. It willalso do its best to help the organisers toraise funds, and is likely to offer somefinancial support to organisers for partici-pants who are young or come fromEuropean countries with financial difficul-ties.

Topics (which may be single or compos-

EMS lecturEMS lectures for 2003es for 2003Call for prCal l for pr oposalsoposals

It appears to me that if one wants to makeprogress in mathematics one should study themasters and not the pupils.

This quotation from Abel was presentedby his first biographer Carl Anton Bjerknesin 1880 [5]. The extract above is fromEdwards [6], who continues:

It is as good an idea to read the masters nowas it was in Abels time. The best mathematiciansknow this and do it all the time. Unfortunately,students of mathematics normally spend theirearly years ..., and make little or no reference tothe primary literature of the subject. The stu-dents are left to discover on their own the wis-dom of Abels advice. In this they are beingcheated [6, p.105].

Edwards further develops his answer towhy should we read the masters? Hequotes André Weil as saying:

As a young normalien I had studiedRiemann, and later Fermat. I was persuadedvery early that diligent attention to the greatmathematicians of the past is a source of inspi-ration ... Having had the benefit of such experi-ence, I naturally found myself led to include his-torical commentaries to put in proper perspectivethe expositions, which were in danger of fallinginto excessive dogmatism ... [6, p.107]

We refer to Edwards for more details ofhis arguments on why we should listen toAbels advice today. The full passage con-cerning this advice in Ores biography ofAbel reads:

I have bought what I believe we do not haveat home, and still have more here, which I willsend in the spring... Among the books is the fifthvolume of the Mécanique Céleste. Perhaps youwill be good enough to deliver it to Hansteenwith my regards ... anyone who has composedsuch a work can look back upon his scientificcareer with satisfaction. Abel confirms his greatadmiration for Laplace in a marginal observa-tion in his mathematical notebook: It is readilyseen that any theory written by Laplace will besuperior to all produced by mathematicians of alower standing. It appears to me ... [11,p.138]

Searching Abels Paris notebook, wefound the marginal comment in French [2,p.79]. Laplace himself, however, is quotedby Kline [8, p.436], saying:

Read Euler, read Euler! He is the master ofus all ...

Euler certainly belonged among themasters that the young Abel had read dili-gently.

For the Nouvelle Edition of AbelsWorks, Weierstrass helped to obtain somematerial from Berlin. After its publication,in a letter to Sophus Lie from April 1882,we find:

... as I learned to know him from CrellesJournal during my student years, this hasbecome of the greatest importance to me ... Therepresentation given by Abel ... became the firstimportant mathematical problem ... which Iluckily could solve. In the 7th semester of myoriginal political science studies I became

absorbed by it, and I decided to devote myself tomathematics ... [7, p.104].

Weierstrasss first publication was onAbelian functions. He was very much afollower of Abel, and according to Mittag-Leffler [9] (see also [12]), he often gave theadvice to his students:

Read Abel, read Abel!For the Weierstrassian rigorous analysis

of today, a good starting point is a detailedstudy of some of Abels letters. We willreturn to this, but to get the appropriatesetting we need some highlights on Abelsmathematical life.

Without Holmboe, no Abel!Niels Henrik Abel was born on 5 August1802 near Finnøy in Norway, but his math-ematical life really started in 1818. Afterspending some school years without show-ing any particular distinction, he got a newmathematics teacher. The young BerntMichael Holmboe, from 1815 also an assis-tant of Prof. Christoffer Hansteen at theUniversity, was only seven years older thanAbel. Through Holmboes new approachto teaching, giving the pupils appropriateproblems to work on in addition to the reg-ular chores, Abels creative talent was real-ly fired. Soon Holmboe had to give himmore.

Together Abel and Holmboe workedthrough Eulers three books on the calcu-lus, which were university texts. Libraryrecords show Abel borrowing NewtonsArithmetica Universalis and PrincipiaMathematica, Gausss DisquisitionesArithmeticae, Lagranges Calcul de Fonctions,and other works of the masters. It is reallyamazing which books and journals wereavailable at the University Library of thisyoung institution, founded only in 1813.Abel himself commented upon this, com-paring his library to those in Copenhagenand Berlin.

Holmboe continued to be his closestfriend, to whom Abel opened up bothmathematically and personally throughouthis life. Mathematically, Abel moved at apace that Holmboe, of course, could notfollow and neither could his universityteachers, the professors Hansteen andRasmusen.

Typical is the story of the quintic equa-tion to prove or disprove the existence ofa general formula for solving polynomialequations of degree 5. Through his read-ing, Abel became acquainted with Cardanoand Bombellis presentation of formulasfor cubic and quartic equations. He quick-ly started to make his own research notes,Mathematiske Udarbeidelser, his first note-book from 1818-20, where we findEquations of third degree and solutions(by Cardan) (see [1, p.139]).

In 1821 he thought he had solved theproblem of the quintic equation. Holmboe,Hansteen and Rasmusen could find no

weakness in his methods, so a short paperwas sent to Professor Degen inCopenhagen for publication as a DanishScience Academy memoir. Degen couldnot point to anything wrong either, but heasked Abel to elaborate it more by givingdetails of an example: x5 2x4 + 3x2 4x +5 = 0. As we know, Abel himself found hismistake.

In 1824 he published his first proof thatit was generally impossible to solve equa-tions of degree 5 in the Cardano-Bombellimanner. Problems involving equationscontinued to be his favorite theme, as Abelwrote to Holmboe from Paris in October1826. Degens reply contained furtherimportant advice for Abel ... to study ellip-tic transcendentals.

This started Abel on his second maincontribution to mathematics. His workwith integrals and elliptic functions, whichled to the famous Paris Memoir and therace with Jacobi. The mathematicaldetails of this area are no longer in currentstandard curriculas. Here we concentrateon the third area in which Abel was inter-ested, and where he is often mentioned asa founder and forerunner of what was tocome, the theory of analysis. But first weneed a few more details on Abels life.

To Berlin and ParisThe Bergen bishop Pavel met ProfessorHansteen in the western part of Norway,and wrote in his diary for July 1821:

... told me about a son of the Pastor Abel ofGjerstad, who now goes to school in Christiania[Oslo], and who is one of the greatest mathe-matical geniuses. When he has passed his exam-en artium, we plan to put together a grant forhim to travel abroad. We expect to see in himone of the worlds best mathematicians ...

The rumour spread. Holmboe,Hansteen and Rasmusen understood thatthey had a jewel in their custody, and theylived up to the responsibilities. On theirstrong recommendation the youngNorwegian university (opened 1813) andthe Parliament (created 1814) gave Abel atwo-year fellowship to go abroad.

Abels first stop was Copenhagen, and

ANNIVERSARY

EMS March 200212

Read the Masters! Read Abel !Read the Masters! Read Abel !Otto B. Bekken

then, with recommendations from theDanish Professor von Schmidten, he wentto August Leopold Crelle in Berlin. Crellewas a famous construction engineer ofGerman railroads and highways, but wasalso very much up to date on current math-ematical research. Meeting Crelle becamea new turning point of Abels life, and theydeveloped a life-long (sic!) intense friend-ship. As we know, Crelle and Abel createdthe first German Journal für die Reine undAngewandte Mathematik. Almost all Abelsworks were published here in the first years1826-29 of the Journals existence (see [10,p.20]).

Abel stayed in Berlin for only fivemonths very important months for ourstory. Here he read Cauchys 1821 AnalyseAlgébrique, and developed further hisstrong admiration for Cauchys work. Hehad already used Cauchys results on per-mutations in his 1824 paper on the quintic.In July 1826 Abel arrived in Paris, his nextmathematical stop. His tragic personalacquaintance with Cauchy is illustratedthrough a letter to Hansteen in August1826:

Finally I have arrived at the focus of all mymathematical wishes, to Paris ... Above all Iwould like to have my memoir completed ... to bepresented to the Institute ... I have the hope thatthe Academy will print it ... [7, p.39].and in one to Holmboe in October 1826:

I showed it to Cauchy, but he scarcely wouldlook at it. Without bragging I dare say it isgood. I am curious to hear the verdict of theInstitute. ... Cauchy is fou, and he is unap-proachable, but he is the mathematician whothese days best knows how to present mathemat-ics ... He is now publishing a series of memoirsentitled Exercises des Mathématiques. I buythem and read them diligently.

Abels Paris Memoir was later describedby Jacobi as the most important discover-ies done in mathematics in this century, byLegendre as monumentum aere peren-nius, and by Picard as there is maybe inthe history of science no such important a

theorem reached through so simple con-siderations (see [7, p.63]). It was present-ed to the Academy on 30 October 1826.Cauchy should have read it and given hisjudgement to the Academy before print-ing, but he never did. A long and excitingstory can be told about the Memoir, endingwith the rediscovery of Abels original in1953 in Biblioteca Moreniana in Florenceby Viggo Brun (see [11]).

The fate of his greatest memoir trou-bled Abel for the rest of his life, until on 6January 1829, from his sickbed at Frolandhe wrote a two-page note on his additiontheorem. The note was published byCrelle in the Journal, and it made Jacobiask for the Memoir, which was finally print-ed in 1841. Without this note from Frolandit probably would have remained inCauchys drawer. Abel also spent somehappy days at Froland. From his notebookduring his summer visit there in July-August 1828, we quote, as his manifesto:

... The situation was that one tried to solvethe equations without knowing that this was pos-sible at all ... and if it then was impossible, onewould search for ever without finding the solu-tion ... Instead of searching by trying or guess-ing how to integrate functions, one shouldrather investigate if it is at all possible to do soin some specified way. If the problem is posed inthis way, it contains the seed for the solution ...I have treated many branches of the analysis inthis way, and even though I often have posedproblems that have exhausted my abilities, Ihave obtained results throwing light on thenature of quantities which belong to the task ofmathematics to study.

EpilogueIn November 1826 Abel returned toBerlin, and in June 1827 was back inChristiania without job or income. He hadoffers from Crelle to remain in Berlin, buthe had to return home! Abel was in lovewith his country always and everywherethinking of how to serve his university andhis friends at home. This is shown by manypassages from his letters.

Abel had no job. He had a chance in1825-26 when Rasmusen became ChiefCashier of The National Bank, but the jobwent to Holmboe. The University adminis-tration wrote (see [7, p.43]):he was not considered so easily able to adjusthimself to the students ability.

In 1828 he finally got to substitute forHansteen, when Hansteen went to Siberiato research on magnetism. The Universityadministration now wrote that they wereextremely satisfied with the easy-to-understandway with which he organises and presents hislectures ...

In the meantime, Abel advertised in thenewspaper for pupils in mathematics both for laggard students and for school-boys preparing for the examen artium.After Abels death at Froland on 6 April1829, one of these students wrote a beauti-ful obituary [11, p.242]:

Many who have been tutored by Abel havedeclared that his presentation was very intelligi-ble, and personally I have the same experience.After having tried in vain to profit from a notvery gifted teachers lectures, I went to Abel and

asked him, if possible, to overcome my aversionagainst mathematics which had resulted from mylong and fruitless efforts. During a threemonths period he proceeded so far that I got intomy head algebra, function theory, ... It is unnec-essary to say that I found his instruction clearand his methods very useful. [11, p.243]

Thus, Abel was also worth listening to,as a teacher!

References1. Niels Henrik Abel, Mathematiske

Udarbeidelser, Notebook from 1818-20, OsloUniversity Library.

2. Niels Henrik Abel, Memoirs de Mathématique,Paris Notebook dated 6 August 1826, OsloUniversity Library.

3. Niels Henrik Abel, Oeuvres Complètes (ed. B.M. Holmboe), 1839.

4. Niels Henrik Abel, Oeuvres Complètes,Nouvelle Edition, 2 vols. (ed. L. Sylow and S.Lie, Christiania, 1881.

5. C. A. Bjerknes, Niels Henrik Abel: en skildringav hans liv og arbeide, Aschehoug 1929 (1st ed.Stockholm, 1880).

6. Harold M. Edwards, Read the Masters! inMathematics Tomorrow (ed. L. A. Steen,Springer-Verlag, 1981, pp. 105-110.

7. Elling Holst, Carl Størmer and LudwigSylow, Festskrift ved 100-aarsjubilæet for NielsHenrik Abels fødsel, Kristiania, 1902 (an edi-tion also exists in French ).

8. Morris Kline, Mathematical Thought fromAncient to Modern Times, Oxford, 1972.

9. Gösta Mittag-Leffler, Niels Henrik Abel, Ordoch Bild, Stockholm, 1903.

10.MA 290: Topics in the History ofMathematics, Unit 14, Algebra and theProfession of Mathematics, by Jeremy Gray,Open University, 1987.

11.Øystein Ore, Niels Henrik Abel: MathematicianExtraordinary, Chelsea 1974 (original inNorwegian, Oslo, 1954).

A more recent extensive biography of Abel is:Arild Stubhaug, Niels Henrik Abel and his Times.Called Too Soon by Flames Afar, Springer-Verlag,2000 (originally in Norwegian, 1996).

ANNIVERSARY

EMS March 2002 13

Vigeland Sculpture of Abel in Oslo

Sir John Kingman is the Director of the IsaacNewton Institute for Mathematical Sciences. ACambridge graduate, he was, successively,Professor at the new University of Sussex,Wallis Professor in Mathematics at OxfordUniversity. In 1985 he became Vice-Chancellorof Bristol University, where he stayed until2001. He has been Chair of the Science andEngineering Research Council, President of theLondon Mathematical Society, and President ofthe Royal Statistical Society.He is the EMS Executive Committees nomineefor EMS President from 2003-06.

What sort of background do you come from?My fathers family come from Somerset inthe West of England, where his father wasa coal miner. My grandfather was adamantthat his two sons should not go down themine, and my father got to the nearbyUniversity of Bristol and became a PhD inchemistry. He eventually moved toLondon to a scientific job with theGovernment and married my mother froma London family. My brother and I werebrought up in the suburbs of London,where I attended a small grammar school.From there I won a scholarship to readmathematics at Pembroke College,Cambridge.

Were there any teachers at school or uni-versity whom you particularly remember?I had several very good teachers at school,and received a lot of encouragement in myambition to study mathematics. AtCambridge I had a number of luckybreaks. In my second year Michael Atiyahjoined the College and supervised my puremathematics: an education in itself. WhenI told him of my interest in probability andstatistics, he arranged for me to be taughtby Dennis Lindley, perhaps the bestteacher of the subject of his generation.There were also a number of quite dread-ful lecturers in Cambridge at that time,who had better remain nameless.

There was very little probability in theCambridge course when you did it. How didyou come to choose to work in probabilitytheory?In my summer vacations I worked in thePost Office Engineering Research Stationon problems in what we would now callapplied probability, especially on conges-tion in telephone systems. I was fascinatedby the mathematical problems that arisefrom stochastic models. In those daysCambridge mathematics was rigidly divid-ed between pure and traditional applied

mathematics, and probability seemed tome to combine the best of deep pure math-ematics and real-world applications.

Who did you do your PhD under?I had planned to work with Lindley, but heleft Cambridge just as I started PhD workin 1960 and I was supervised by PeterWhittle. After a year he left too, and sug-gested that rather than following him toManchester I should go to Oxford to workwith David Kendall. I spent a year inOxford, at the end of which David waselected to a new chair in Cambridge, and Ireturned with him as a member of theteaching staff. So I never finished my PhD.

Did switching supervisors mean that youhad to switch problems?My work on queueing theory had led me tomore fundamental problems in Markovchain theory, and to what became the the-ory of regenerative phenomena. There wascertainly a change of emphasis, and I wasvery much influenced by David Kendall, inmathematical style and taste as well as insubstance. Although I was no longer hisstudent, I worked closely with him until Ileft Cambridge for the new University ofSussex in 1965.

Did you enjoy a new university untram-melled by tradition?Sussex in the 1960s was a very excitingplace, alive with new ideas and opportuni-ties. My wife was teaching history there,and we made many friends across thewhole range of subjects.

In 2002 the new universities of the 1960sare often difficult to distinguish from theirolder brethren. Have they added anythingpermanent to the system?All British universities were affected by thenew departures taken by Sussex, Warwickand the other new universities. Many of thethings we now take for granted in tradi-tional universities were pioneered by theseuniversities, especially in new subjects andinterdisciplinary collaboration.

After four years at one of the newest uni-versities you went as professor to the oldestin England. How did Oxford contrast?Statistics in Oxford in 1969 was frankly amess. There was no professor of statistics,the only chair having been abolished someyears before. The only statistician who helda chair was Maurice Bartlett, who wasProfessor of Biomathematics and was sup-posed to concentrate on advising biologistsabout their statistical and mathematicalproblems. I was appointed Professor ofMathematics to raise the profile of proba-bility theory (but not statistics) in theFaculty of Mathematics. Of course,Maurice (and his successor Peter Armitage)and I conspired to persuade Oxford to

INTERVIEW

EMS March 200214

Interview with Sir John KingmanInterview with Sir John KingmanInterviewer: Tom Körner (Cambridge)

take statistics seriously, and now there is aproper statistics department teachingmathematicians and non-mathematicians.

The local problems in Oxford do reflect amore global problem in integrating mathe-matics and statistics. Statisticians often feelhard done by in traditional mathematicsdepartments and press for separate depart-ments, courses and degrees. What do youfeel about this?Remember that statistics is not a subset ofmathematics, and calls for skills and judge-ment that are not exclusively mathemati-cal. On the other hand, there is a largeintersection between the two disciplines,statistical theory is serious mathematics,and most of the fundamental advances,even in applied statistics, have been madeby mathematicians like R. A. Fisher. It isimportant to expose students of mathe-matics to statistics, which many will chooseas a career. There is no easy way to achievethe right structure in a university, and nosingle optimal solution.

Which of your mathematical results are youproudest of?The one that has given me most satisfac-tion, and which I think lies deepest, is thecharacterisation of diagonal Markov tran-sition probabilities. It is part of the theoryof regenerative phenomena which I intro-duced, although it was inspired by DavidKendall, and which is I think an importantarea of the theory of random processes.

The result which has been most influen-tial is undoubtedly the subadditive ergodictheorem, conjectured by JohnHammersley and Dominic Welsh. Theyrightly saw that it would have a wide rangeof applications, and I was lucky enough tofind a proof.

In terms of applications outside mathe-matics, my early work on queues in heavytraffic is now a standard part of opera-tional research. Some biologists believethat some of my results in populationgenetics, especially a Markov process onequivalence classes of finite sets called thecoalescent, are important for the under-standing of genetic diversity.

How did you move into administration?I got involved in the peer review work ofthe Science and Engineering ResearchCouncil, first in mathematics and thenmore widely, and in 1981 was invited tobecome its Chairman. I enjoyed the prob-lems of research funding across a broadrange of subjects, and when in 1985 I wasasked to head the University of Bristol Iwelcomed the opportunity to lead a greatresearch university.

Most mathematicians claim both to despiseadministration and to be bad at it. Why doyou differ?There are plenty of counterexamples toyour assertion. In Britain alone PeterSwinnerton Dyer was in charge of thewhole university system, and MichaelAtiyah was a very successful President ofthe Royal Society. In my experience manymathematicians have proved good leaders,

and I should be surprised if this were neg-atively correlated with mathematical abili-ty. Of course, an affectation of incompe-tence can be a useful defence mechanism.

A modern vice-chancellor not only has totake a lot of hard decisions but acts as afocus of resentment for many members ofthe university. Did you find it hard to takethe personal animosity?It is no good becoming a vice-chancellor ifyou want to be loved. On the other hand,you can be respected as someone with theinterests of the university at heart, and assomeone whose decisions are seen to befair and considered. In practice, I found itpossible to get on well with people withwhom I disagreed about important issues.

Which decisions that you took as vice-chan-cellor are you most satisfied with? Which doyou most regret?My best and my worst decisions had to dowith the appointment of particular profes-sors. It is the most important job of a vice-chancellor to appoint the best possible aca-demic leaders: there can be no good uni-versity without good professors.

Was it possible for you to keep up yourmathematical interests as vice-chancellor?Yes, but not as much as I would have liked.

You have now moved to be Director of theIsaac Newton Institute in Cambridge. Is itan easier job?A very different job, but very challenging.The success of the Institute depends onchoosing the most exciting fields of pureand applied mathematics several yearsahead, and then attracting the best mathe-maticians from all over the world. My pre-decessors Michael Atiyah and KeithMoffatt have set me a very high standard.

People sometimes fear that the mathe-matical world will become divided into anélite group of researchers jetting every sixmonths from one research institute toanother and a lumpenproletariat of teach-ers.

Do you think this is likely to happen?No. If you look at the lists of visitors to the

INI, you see that most of them are in uni-versity teaching positions to which theyreturn mathematically refreshed.

Even if the Newton Institute works on aninternational scale does it work at a Britishlevel? Can ordinary lecturers at a Britishuniversity really find the time and resourcesto join one of your programmes?We have asked this question, and the evi-dence so far is that they can. If we find evi-dence to the contrary, we shall approachour funders to seek resources to improvethe situation.

You are Chairman of the StatisticsCommission set up by the UK Governmentto keep official statistics honest. Is this tasknecessary? Can the Commission succeed init? And should this be its main task?There is a job to be done, both in ensuringthe integrity of Government statistics, andin countering widespread scepticism alongthe lines of the sneer (attributed by MarkTwain to Disraeli) Lies, damned lies andstatistics. Only time will tell whether wecan succeed, but I am hopeful.

Finally I would like to ask about theEuropean Mathematical Society itself. Whydo you think it is necessary?Because we live in a world in which increas-ingly decisions affecting the mathematicalcommunity are made at a European level.There is a pressing need to raise the pro-file of mathematics with those who takethese decisions. There is much else that theEMS can and will do, but its most impor-tant job is to argue the case that mathe-matics is essential and must be supported.If we do not hang together, we shall hangseparately.

Some people see the EMS as a child whichwill grow up to be something like the AMS.What do you think?The American Mathematical Society is avery successful operation in the US con-text. The EMS can certainly learn from theAMS, but Europe is not America. Forinstance, many countries have their ownsuccessful mathematical societies which theEMS must complement, not try to replace.

INTERVIEW

EMS March 2002 15

Isaac Newton Institute for Mathematical Sciences

Part 1 of this interview appeared in the previ-ous issue.

Tell us about how you took your first stepsinto new areas.The lack of serious interaction betweenmathematicians and mechanicians in mod-ern theoretical physics was a failure of theMoscow State University Department ofMechanics and Mathematics in the 1950sand 1960s.

I had the opportunity to get acquaintedwith the foundations of mechanics andwith the theory of incompressible fluid atseminars by friends of mine, and this wasall I could get in this direction at the

Department of Mechanics andMathematics.

I heard in Gelfands circle that quantummechanics conceals beautiful mathematics.I also heard from my brother [the physicistLeonid Keldysh] that quantum field theorywas of great importance.

In the mid-1960s, influenced by theprogress in the theory of elementary parti-

cles, the community of physicists thirstedto study modern mathematics. In turn, Ialso had the desire to study these branchesof theoretical physics.

I started with statistical mechanics andquantum field theory and quickly under-stood that no success can be achieved thisway: it is necessary to learn the materialstep by step from simple ideas to compli-cated ones. In due time, this scheme wasthought through by Landau. Togetherwith Lifshits they wrote a series of text-books forming a high road for studyingtheoretical physics (though it is useful tostudy some parts by using textbooks ofother authors): it is necessary to begin with

Mechanics, then to proceed with Field theoryand Quantum mechanics, and only after thatshould one study Statistical mechanics andQuantum field theory. It is also good to learnHydrodynamics, Elasticity theory, Physics ofcontinuous media, and Kinetics.

Following this path for some years, Idecided to begin an active interaction withphysicists of the Landau school at the end

of the 1960s. Experts in theoreticalphysics heard something about topologyand wanted to get acquainted with it. Aftera period of study I faced the same problemas that at the end of the 1950s: how shouldI start?

What was your first work in these newareas?I was interested in Einsteins general rela-tivity. I was deeply impressed by the fun-damental discovery in this area that ouruniverse is far from being eternal, livingonly 10-20 billion years, while continuous-ly expanding.

Khalatnikov asked me to give a carefulperusal of their researches devoted to thestate of the universe in the vicinity of a sin-gularity. Together with my discipleBogoyavlenskii, I wrote a series of papersdevoted to anisotropic perturbations of thestandard model of the universe. We man-aged successfully to apply the technicaltools of working with many-dimensionaldynamical systems: I took the ideas ofthese tools from my participation in theseminars of my friends at the Departmentof Mechanics and Mathematics in the1960s. However, the mathematicians inour department chose only things thatcould be rigorously proved, while we hadto extend these limits.

It soon became clear that it is senselessto consider the cycle of compression thatpreceded the current expansion because,after a small perturbation, an isotropiccompression achieves a Belinskii-Lifshits-Khalatnikov complicated regime with acomplicated singularity that cannot beextended anywhere. We found out that theobservable isotropy of the expanding uni-verse does not follow unambiguously fromthe laws of the Einstein classical generalrelativity, in any natural statistical settingwith initial data at an early stage if the mat-ter is in some state accessible to the under-standing of modern physics.

However, modern astronomical obser-vations lead to the conclusion that the uni-verse had already become isotropic at avery early inflationary stage in which thesubstance was in a mysterious condition.This certainly decreased the value of worksdevoted to non-isotropic cosmologicalmodels.

I stopped my work in this area,although friends and colleagues(Zeldovich, Khalatnikov, I. D. Novikov,and others) invited me to turn to quantumgravity with them, because I could notbelieve that a quantisation of the Einsteingravity is really necessary: the scales atwhich this quantisation must take place aretoo fantastic and unattainable.

How did you change to soliton theory, where

INTERVIEW

EMS March 200216

Interview with SerInterview with Sergey Pgey P. Novikov (part 2). Novikov (part 2)Interviewer: Victor M. Buchstaber (Moscow)

S.P. Nonikov

so many important results are due to you?Working in a circle of physicists in 1973, Igot acquainted with the remarkable math-ematical ideas of soliton theory namely,with the method for the inverse scatteringproblem, which had been discovered as aresult of the joint activity of experts in the-oretical physics and mathematicians in the1960s. This method worked successfullyfor solitons that is, for solutions of thewell-known KdV (Korteweg-de Vries) equa-tion with rapidly decreasing initial data.

Is it possible to develop the correspond-ing periodic analogue? Since 1974 I havedevoted my energies to this very problem.My discovery consisted in the close unitybetween the following branches of mathe-matics: the spectral theory of operatorswith periodic coefficients on the line, thetheory of completely integrableHamiltonian systems, and analysis onRiemann surfaces (that is, algebraic geom-etry). The main role in the construction ofexact solutions of the KdV equation isplayed by the Hill operators orSchrödinger operators on the line with theremarkable finite-zone property.

As I proved, this property of the spec-trum follows from a purely algebraicassumption that a periodic differentialoperator is algebraic: this means thatthere is another differential operator thatcommutes with the given one.

The theory of finite-zone operators wassoon completed by me and my discipleDubrovin, and also by Matveev and Its,who actively joined the development ofthese ideas after my first work on thistopic. Soon, in 1975, a part of these ideaswas independently found in USA by Lax,McKean, and van Moerbeke.

Already, by 1974, Shafarevich hadbrought my attention to the fact that theseconstructions lead to new results, even inalgebraic geometry per se, giving an explic-it rational realisation of the entire space ofmodules of hyperelliptic Jacobians. Thesemethods can be transferred without anymodification from the Korteweg-de Vriesequation to all one-dimensional systemsintegrable by the method of solitons.

For spatially two-dimensional systems(such as the Kadomtsev-Petviashvili equa-

tion), the situation turns out to be veryinteresting. The development of thismethod, which was realised in this case byKrichever (1976-77), required the totalalgebraisation of the procedure to releaseit from both the Hamiltonian systems andthe self-adjoint operators: you obtain solu-tions of the KadomtsevPetviashvili equa-tion by using only data from algebraicgeometry..

This was a decisive step in understand-ing the connections between solitons andcomplex algebraic geometry. At the sametime, the method presents difficulties: weface the problem of singling out real solu-tions having physical sense: for example,for the famous sine Gordon equation, theproblem of the theory of real periodic solu-tions have remained open. Problems ofthis kind can be solved readily and effec-tively only within the framework of the the-ory of self-adjoint operators, but this is notthe case for the sine Gordon equation.Grinevich and I are now making seriousprogress here.

Later on, many works devoted to thedevelopment of these ideas were complet-ed at my seminar. Krichever, Dubrovin,Veselov, Bogoyavlenskii, Taimanov andGrinevich took part in it.

What were the most fundamental directionsthat you developed here?I would like to mention the followingdirections:The inverse problem for a two-dimensionalSchrödinger operator for a fixed energy. Westarted developing this direction withManakov, Dubrovin, and Krichever in1976, but the most interesting soliton sys-tems were found by Veselov and me lateron, in 1984 (the Novikov-Veselov hierar-chy).The problem of classifying the commuting oper-ators with rank greater than 1 and the defor-mations of holomorphic bundles over algebraiccurves (Krichever-Novikov equations and thesolutions of the KP equation of high rank).This theory was created in 1978-80 in col-laboration with Krichever, and Grinevichand Mokhov also took part in it.Difference analogues of this theory weredeveloped quite recently by Krichever andme: by the way, Krichever has beautifullyapplied these ideas to the investigationand generalisation of the so-called Hitchinsystems.Universal approach to the Hamiltonian formal-ism of systems integrable by methods of algebra-ic geometry that is, the so-called algebro-geo-metric Poisson brackets. This direction wasdeveloped by Veselov and me in 1982-84.As Krichever and Phong indicated severalyears ago, similar symplectic structuresmysteriously arise in Seiberg and Wittensworks on the supersymmetric Yang-Millstheory (for N = 2).Analogues of the Laurent-Fourier bases onRiemann surfaces namely, Krichever-Novikovbases and algebras, and the operator quantisa-tion of a bosonic string. This direction wasdeveloped by Krichever and me in 1986-90.

This is the list of directions in solitontheory that I developed with my disciples

and in which methods of algebraic geome-try were intensively applied.

What about your conjecture giving a solu-tion of the classical Riemann-Schottkyproblem by soliton methods?For some years in the late-1970s I closelyexamined the formulas of Its-Matveev typefor solutions of the KdV equation and ofKrichever type for solutions of the KPequation. They are of the form u(x, y, t) =2∂2/∂x2 log θ(Ux + Vy + Wt + Z; B) + const.I asked myself: Is this expression an effec-tive formula, as is the case in classicalanalysis? I decided that it isnt.

We do not know in which cases thematrix B is determined by a Riemann sur-face, and this is precisely the RiemannSchottky problem. Moreover, the vectorsU, V, and W must be connected with thematrix B by complicated relations thatnobody understands.

How one can make such formulas effi-cient? My idea was that one should initial-ly regard the matrix B and the vectors U,V, and W as independent variables. Allrelationships among them must followfrom the requirement that the entireexpression satisfies the simple universalKP equation. If this is the case, then weobtain a significant effectivisation of the θ-functional calculus and of the solution ofthe Riemann-Schottky problem.

The first important result in this direc-tion was obtained by Dubrovin in 1981; itwas considerably strengthened byArbarello and De Concini (1984). My con-jecture was completely proved by Shiota(1986). This approach, starting withDubrovin, was repeatedly used in solitontheory for practical effectivization of θ-function formulas. An analogue of thisconjecture was investigated by Taimanovfor Prym θ-functions. In this case the KPhierarchy must be replaced by the so-called Novikov-Veselov hierarchy relatedto a two-dimensional Schrödinger opera-tor.

How about methods of Riemannian geome-try in the theory of systems of hydrodynamictype. What are the Dubrovin-Novikovbrackets?Since the early 1980s, I was interested inPoisson brackets in hydrodynamics underthe influence of a circle of Landau disci-ples, Dzyaloshinskii and Khalatnikov. Itturned out that Landau already knew thesebrackets by 1940 when trying to quantise afluid. Two directions of my scientific worksactually arose from this source of ideas: themany-valued calculus of variations and thetheory of systems of hydrodynamic type.

Quasi-linear homogeneous systems offirst-order differential equations (systemsof hydrodynamic type) have been studiedsince Riemann, in connection with hydro-dynamics of compressible fluid. Dubrovinand I investigated the following problem:when is such a system Hamiltonian?Physical systems of this kind usually arisewhen describing an inviscid fluid, and it isnatural to expect that they must beHamiltonian. (We should not mix up thisproblem with the possibility of represent-

INTERVIEW

EMS March 2002 17

Victor Buchstaber with Sergey P. Novikov

ing a system as a subsystem or quotient sys-tem of a Hamiltonian system, because thisis always possible.)

In 1983 we introduced a class of brack-ets of hydrodynamic type which gives anatural answer to the question: thesebrackets are based on Riemannian geome-try. For diverse reasons, our discovery hadmany consequences. Many new importantsystems of hydrodynamic type arose in the1970s and 1980s from soliton theory Whitham (1971), Flashke-Forest-McLoughlin (1980), etc. to solve asymp-totic problems by using the scheme ofnon-linear semi-classics, successfullyapplied by physicists (Gurevich-Pitaevskii,1973). When proving my conjecture, thepostgraduate Tsarev successfully appliedour Hamiltonian formalism and construct-ed a scheme for exact integration ofHamiltonian systems of hydrodynamictype on the basis of differential geometry(1985). Later, in the second half of the1980s, as a result of a numerical and ana-lytical researches in which Avilov,Krichever and Potemin worked with me,we combined this technique with analysison Riemann surfaces and analyticallyexactly solved the problem of the dis-persed analogue of a shock wave, whosestudy was begun by physicists in 1973.

In our works in the 1980s, a lot of beau-tiful mathematics appeared, both algebraand geometry, which was used by Dubrovinin the 1990s in the topological two-dimen-sional quantum field theory. These ideashave recently been successfully applied inthe classical problem of orthogonal coordi-nates on flat spaces (Dubrovin, Zakharov,and Krichever).

Very interesting non-local extensions ofPoisson brackets, whose investigation wasstarted by Mokhov and Ferapontov (alsoparticipants at my seminar) have increasedthe abilities of the method. These exten-sions still attract our attention. I note that,generally, the appearance of a lot ofdiverse important Poisson brackets, theknack of using them, and the understand-ing of their role in modern science areamong the achievements of soliton theory.After this theory it became clear that thelocal Poisson structure is the major prima-ry object in theoretical physics, while thesymplectic structure is preferable in puregeometry.

What is the many-valued calculus of varia-tions (the Morse-Novikov theory and theNovikov ring)? How is it related to theWess-Zumino-Novikov-Witten quantumfield model?The many-valued calculus of variations isalso rooted in my Hamiltonian researches.Examining textbooks in hydrodynamics, Iobserved in 1981 that the so-calledKirchhoff equation for the free motion ofa rigid body in an ideal incompressiblefluid is a Hamiltonian system on the Liealgebra of the isometry group of three-dimensional Euclidean space.

Apparently, this fact was not mentionedearlier. Mechanicians soon pointed outthat the equations of motion of a top thatis, a rigid body in a gravity field with a

fixed point can also be represented in asimilar form. I noted that this system canbe reduced to the motion of a charged par-ticle along the surface of the two-dimen-sional sphere (with some metric) in anexternal magnetic field with non-zero flowthrough the sphere. This situation is like aDirac monopole! Certainly, the physicalmagnetic field is absent here; however,mathematically, a magnetic field turns outto be equivalent to the correction ofPoisson brackets (symplectic structure) thatoccurs in the reduction of the system.

Intending to develop something similarto Morse theory for finding periodic orbitson the sphere (that is, 2-tori of an initialsystem), I understood that the mechanicalaction of the above system on the sphere isnot defined as a single-valued functional:only its variation is correctly defined as aclosed 1-form on the space of closed paths.I was amazed by this simple fact, andimmediately understood its fundamentalrole in mathematics and theoreticalphysics. Neither the calculus of variationsnor field theory discussed this possibility.As a corollary, I came to the following con-clusions:(1) In quantum mechanics and quantumfield theory, a topological quantisation ofthe coupling constant arises, based on therequirement that some 1-form, the so-called variation of action, defines an inte-gral 1-cohomology class of the space offields (under appropriate normalisation).This is necessary for the Feynman ampli-tude to be a single-valued functional. It isinteresting that Diracs idea was different:he started from the Schrödinger formalismand (in modern language) required thatthe magnetic field must be the Chern classof a bundle whose fibres give the Hilbertspace of states. The new approach is muchmore convenient for generalising the Diracmonopole to quantum field theory. I gavea classification of all local Lagrangians offield theory that lead to non-trivial 1-forms. It later emerged that, when evalu-ating anomalies in the Yang-Mills theoryseveral years earlier, Wess and Zumino hadobtained a Lagrangian that was a special

case of those above, but saw no analogywith the Dirac monopole and carried outno topological analysis. Some physicists Deser, Jackiw, Templeton (1982), andWitten (1983) arrived at related ideas indiverse examples soon after me.(2) It turned out that there is a many-val-ued analogue of Morse theory for closed 1-forms on finite-dimensional manifolds;however, instead of usual CW complexes,the gradient of a 1-form generates com-plexes over specific rings, which were lateron called Novikov rings and used for thehomology theory of Floer type, where theanalysis is more complicated but the heartof the problem is the same namely, 1-forms occur instead of functions.(3) In collaboration with my disciples(Taimanov and Grinevich), I also obtaineda series of results on periodic orbits in amagnetic field. Some deeper observationsare still insufficiently justified; here thereare interesting mathematical problems.

What scientific and pedagogical ideasunderlay the book series Modern geome-try?. Is this programme complete, or doyou plan a further development of thisseries?Many years ago, in the 1960s, I formulateda plan to present modern topology, creat-ed since the early 1950s, in the education-al literature: in my opinion, this is a greatachievement of 20th-century mathematics.Until the second half of the 1960s, the bestachievements were reasonably presentedin the original works, such as those byPontryagin, Serre, Cartan, Thom, Milnor,Smale, Atiyah, Hirzebruch, I alwaystried to follow their example, to write largeworks that are as clear as possible. Thetopological achievements of that timecould be learnt from these works.

However, a formalised abstract stylethat unnecessarily complicated the exposi-tion for algebraic formalism had alreadyappeared during this period. It is very dif-ficult to understand the core of the subjectfrom such texts. This style gradually beganto appear in topology, and not only topol-ogy. Besides, starting from the late-1960s,

INTERVIEW

EMS March 200218

Sir Michael Atiyah and S.P. Novikov

several of the best papers remaineduncompleted by their authors, but this wasnot understood by a wide community atleast, no publicity was given to this fact. Itbecame clear that there can be no seriousdevelopment in an area that cannot belearnt, and in which one cannot separateknown facts from unknown ones.

For many years, I brought up good dis-ciples. They developed in seminars atwhich training problems were solved andthe key ideas of topology were investigat-ed. I gave a series of courses whose mate-rial was carefully repeated. Besides, myjoint work with mechanicians and physi-cists in the 1970s, and the study of theseareas, induced me to think deeply aboutthe creation of courses that could serveboth communities, mathematicians andexperts in theoretical physics. Fomenkohelped me to introduce the elements ofgeometry and topology to mechanicians. Idrew up a plan for a series of books whosebeginnings we had already, and alsorecruited Dubrovin. In collaboration, wewrote a series of books Modern Geometry inthree parts. According to the plan, Part I(geometry to topology) should accustommathematicians to the elements of naturalsciences, create bridges with theoreticalphysics, and accustom them to geometryand the ideas of field theory. Part II (thedifferential approach to topology) shouldbe an understandable and useful course oftopology, both for physicists and mathe-maticians working in different areas ofanalysis, and a unification of topology witha world of other areas of science that areless abstract. Part III contained the ele-ments of modern algebraic topology. Theseries should have been continued, andPart IV should be written to fulfil the plan,but we had neither strength nor time to doso.

Later on, it turned out that the commu-nity of topologists and geometers was nottoo much interested in unification with thenatural sciences: Part I was spread insuffi-ciently widely among mathematicians.Taimanov and I are now writing a newtextbook that greatly modernises the ideasof Modern Geometry I. I hope its a goodtime for this topic to be studied by a broadcommunity of mathematicians. Part II wasmore successful, and quite broad collec-tions of mathematicians, experts in mathe-matical physics, and students have studiedthis book. As to Part III, it should be notedthat education in the area of high topolo-gy had generally declined badly in the lastthirty years, and currently the potentialreaders of Part III form a rather limitedcommunity of very particular experts.

With Fomenko, I also wrote an elemen-tary textbook, and an encyclopaedic bookTopology I (English translation in theEncyclopaedia of Mathematical Sciences, Vol.12, Springer, 1996), which, in my opinion,transparently and clearly presents theentire cycle of ideas of classical topologyup to the early 1970s. My other educa-tional books (Soliton Theory, written with agroup of physicists, and a volume of theEncyclopedia under the title DynamicalSystems, Integrable Systems, and Symplectic

Geometry (English translation in theEncyclopaedia, Vol. 4) are devoted to otherareas; their major problem is a ratherbroad introduction into a new techniquedeveloped with my disciples: the solutionof periodic problems of soliton theory andthe spectral theory of operators that comesfrom the analysis on Riemann surfaces andalgebraic geometry is one of the mainexamples. Algebraic geometers aspire toconvert it into something abstract, whilescientists who effectively use classical analy-sis cannot study it without difficulty, andthus the process of assimilation is verycomplicated.

What are your views on contemporaryphysics and mathematics education? Manypeople have heard that you speak about acrisis of physical and mathematical com-munity.My experience, my long-term connectionwith education, tells me that an activeprocess of reducing the level of physics andmathematics education began in the last

decade (and possibly earlier). Such aneducation no longer produces scientistswith a broad profile. The process gears up.I wrote some papers on the subject. It ispossible to speak even about a deep crisisin our areas of science. Recently I wrote anew paper (in Russian) about this crisis: itis not published yet, but can be found onthe internet.

It is a very serious problem that cannotbe elucidated in two words. Theoreticalphysics declines most rapidly. Pure math-ematics turns out to be steadier for now:though it also declines, it has more chancesto survive and stay at the same high level.It is possible that some fundamentalachievements of the second half of the20th century that are mathematical inessence and made by experts in theoreticalphysics for example, modern quantumfield theory will be saved for the future asparts of mathematics. However, mathe-maticians must at first study these achieve-ments.

Based on this assumption, I would liketo write manuals to prepare mathemati-cians in the elements of this area.

However, the study of this subject requiresvery serious preparation, and one should-nt begin with it. Many people do notunderstand this rule: everybody knows, forinstance, that its impossible to build ahouse starting from the tenth floor, butsome people still do not apply this analogyto science. It is also absurd to try to pre-sent this totality of knowledge in a super-formal algebraised language, since thematerial would become so complicatedthat nobody could learn it.

For more than ten years (1985-96) you werePresident of the Moscow MathematicalSociety, whose role in the creation of thefamous Moscow mathematical school of the20th century has been written about manytimes. What can you can tell us about this,and what is the role of the Society now?Yes, the Moscow Mathematical Society,which is the mathematical face of theDepartment of Mechanics andMathematics, is the main scientific arenafor the mathematicians of the Moscowschool, whatever they work on.

Our society was founded in the 19thcentury, but it progressed as a consequenceof the development of the Moscow mathe-matical school in the 1910s and 1920s,especially when the presidents wereZhukovskii and Egorov, the founders ofoutstanding schools of mechanicians andmathematicians. The Egorov-Luzin schoolbecame famous all over the world anddetermined the face of Moscow mathemat-ics in the 20th century. In Moscow, allmathematical activity in the 1920s and1930s was concentrated around theSociety, being interrupted sometimes byperiods of hunting by the Soviet system forintellectuals for example, during 1929-33. So it was till the mid-1950s. Since themid-1960s, after passing through a diffi-cult period, the Society has won back itsposition as a central forum for Moscowmathematicians, and has successfully keptthis ever since.

Let me list some recent Presidents: P.Aleksandrov (1933-64), Kolmogorov(1964-66 and 1973-85), Gelfand (1966-70), Shafarevich (1970-73), Novikov (1985-96) and Arnold (1996-).

In the late Bolshevic period of the1970s, marked by severe anti-Semitism as astate policy and persecution of liberalintellectuals, our Society faced great diffi-culties. In the 1980s, the connection withMGU was weakened, where an anti-scien-tific approach had prevailed, especially atthe Department of Mechanics andMathematics the more so, since the lead-ership of MGU began unskilfully to dis-prove Einsteins general relativity, etc.However, we managed to keep our scien-tific face.

After the disintegration of the USSR inthe early 1990s, we reorganised andstrengthened our connection with theSteklov Institute, where a process ofrenascence took place; much was done byus at this time to create and stabilise theIndependent University. This work hasproceeded quite successfully in the last fewyears.

INTERVIEW

EMS March 2002 19

The Union of Czech Mathematicians andPhysicists is one of the oldest learned soci-eties in the Czech Republic. It will cele-brate 140 years of its existence in 2002.

HistoryLet us start with a brief survey of the devel-opment of the activities in mathematics andphysics in the region that is now occupiedby the Czech Republic.

The eldest educational institution in thearea is the Charles University, which wasfounded by the Holy Roman EmperorCharles IV in 1348. However, teaching ofmathematics and physics of significancebegan only around the middle of the 18thcentury. At that time, polytechnic institu-tions were founded in Bohemia, and the so-called Royal Czech Learned Society was estab-lished. (We recall that Bohemia was anintegral part of the Austrian later Austro-Hungarian Empire until 1918.)

Several outstanding scientists lived andworked in Prague in those times in par-ticular, Stanislav Vydra (1741-1804),Bernard Bolzano (1781-1848) andChristian Doppler (1803-54). With thegrowing interest in activities and teachingof mathematics and physics, demandincreased for a society that would supportthe developments of research and teachingin these sciences, in particular among stu-dents. As a result, on 28 May 1862, theSociety for Open Lectures in Mathematics andPhysics in Prague was founded, and on thisday our Union came into existence. Soon,the Union obtained support from universi-ty teachers, the most important of whom

were Filip J. Kulík (1793-1863), Ernst Mach(1836-1916) and Augustin Seydler (1849-91).

In 1863, Professor Kulík donated to theSociety a good part of his enormous math-ematical library; the remaining part wasinherited by the Society after his death. In1868, Professor Mach offered the Societyhis lecture theatre for meetings and his lab-oratory for physical experiments. In 1869,the Austrian police headquarters registeredthe society (having by this time 69 mem-bers) under the new name Union of CzechMathematicians.

In the first years of its existence theUnion made a significant contribution tothe creation of mathematical and physicalterminology in the Czech language, and on5-6 August 1870, it organised the first con-gress of Czech physicists and mathemati-cians.

In 1872, on the 10th anniversary of theestablishment of the Society, the first num-ber of a new journal was issued. The journalwas called Èasopis pro pìstování matematiky afysiky (Journal for the Cultivation ofMathematics and Physics), and was pub-lished continuously (with a forced breakduring World War II) until 1951, when itwas split into Èasopis pro pìstování matematiky(Journal for the Cultivation of Mathematics in 1991 renamed as MathematicaBohemica) and Èeskoslovenský èasopis profyziku (Czechoslovak Physics Journal).

In 1873 the Union began to publishtextbooks in mathematics and physics, andin 1892, a Supplement for High-SchoolStudents, was included in the membershipjournal: at that time, this was quite an inno-vative idea.

At the beginning of the 20th century,there was a further blossoming of mathe-matics and physics. The Union was a cen-tre for discussions, sparked by a strongmovement towards the reform of educationin mathematics and the other sciences.The number of Czech secondary schoolsbegan to grow in Bohemia and Moravia,and some of the founders of the Uniongained recognition for this.

The Unions branches outside Praguesoon began to grow. The most importantof these were those in Brno and Bratislava,established in 1913 and 1929, respectively.

In 1911, departments of theoreticalphysics were opened at both parts of theUniversity, which since 1882 had beendivided into Czech and German parts.Albert Einstein (1879-1955) was living andworking in Prague during the years 1911-12.

After World War I the Union becamepractically the only publisher of textbooks,monographs and journals in mathematics,physics and related sciences. In 1919, theUnion obtained a license for printing, pub-

lishing and selling books, purchased aprinting house and established its ownPublishing House and bookshop.

The establishment of Czechoslovakia in1918 brought important changes in mathe-matics and physics. In 1921, the Faculty ofSciences separated from the Faculty ofHumanities. The Prague Polytechnic wasreorganised and called the CzechTechnical University. In the same year, theUnion changed its name to the one it bearstoday.

During the twenty years of independent

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EMS March 200220

The Union of CzechThe Union of CzechMathematicians and PhysicistsMathematicians and Physicists

Lubo Pick

The logo of the Union.

The house in itná Street 25, bought by theUnion in 1930. At the rear, the Union erecteda modern building, housing the bookshop andlater the library of the Union. The house nowhas one more floor (built in the early 1990s)and is occupied by the Mathematical Institute ofthe Academy of Sciences of the Czech Republic.

Postage stamps released in 1962, 1987 and 2000.

Czechoslovakia, the number of members ofthe Union rapidly increased, as did thescope of its activities. In 1933, the UnionsPublishing House merged with Prometheus,the Publishing House of mining engineers,thereby establishing a publishing centre fortechnical literature. In 1935, the Unionstarted to run a society for the productionof tools for science and education. In 1938the house in itná 25 was built, and theUnion moved its headquarters there; thebuilding currently houses the MathematicalInstitute of the Academy of Sciences of theCzech Republic.

During World War II the Czech univer-sities were closed by the Nazis. In this dif-ficult period the Union did the best it couldto convey information of new results to theyounger generation by organising variouscourses and publishing monographs writ-ten in a generally understandable manner,even though the publication of the mem-bership journal was forbidden by the Nazis.

In 1948, the Communist regime tookover power in Czechoslovakia. One of itsfirst steps was a forced nationalisation or

rather, confiscation of all private property.As a result of this process, the Union lost itsPublishing House, library and bookshop.

In the early 1950s the CzechoslovakAcademy of Sciences was established, andthe Union became a learned societyattached to the Academy. The Unionsproperty was transferred to the Academy;in particular, the mathematical part of theUnion library became the basis for thelibrary of the Mathematical Institute of theAcademy, where it has been taken care ofever since.

In 1962, the Union convened itsCentenary Congress: a commemorativepostage stamp was released by theCzechoslovak Mail on this occasion.

In 1968, the Physical Research Sectionwas established, and through its represen-tation the Union became a member of theEuropean Physics Society.

In 1969 a federalisation process tookplace in Czechoslovakia. As a consequence,the Union of Slovak Mathematicians andPhysicists began.

In 1987, the 125th anniversary of theUnion was celebrated in Prague. TheCzechoslovak Mail released three postagestamps, and the Union released a

Commemorative Medal that has been usedever since.

In 1990 the Union became a foundationmember of the European MathematicalSociety, through the representation of theMathematical Research Section, and in1992 the Union became a reciprocity mem-ber of the American Mathematical Society.

In 1993 the Union attempted (withoutsuccess) to regain its confiscated property.

In 2000, the Mathematical ResearchSection organised a number of propagandaevents commemorating the World Year ofMathematics 2000; another postage stampwas released by the Czech Mail.

Structure and organisationThe Union has about 2500 members, morethan half of them being secondary schoolteachers. The supreme body of the Unionis the Union Congress, which is convenedevery three years. In between Congresses,the activities are supervised by the CentralCommittee, headed by the President of theUnion. The past presidents of the Unionhave been significant scientists and impor-tant personalities in Czech or Slovak scien-tific life, including Bohumil Bydovský,Vladimír Koøínek, Frantiek Závika,Miroslav Valouch, Josef Novák and IvanÚlehla, to name just a few. The currentPresident of the Union is a distinguishedCzech mathematician, Professor JaroslavKurzweil.

The Union has 15 branches in allregions of the Czech Republic. Aside fromthe branches, the Union is divided intofour sections the Mathematical ResearchSection, the Physical Research Section, theMathematical Pedagogical Section and thePhysical Pedagogical Section. Each sectionhas its own structure and bodies, and alsoits own membership bulletin providing themembers (and others) with informationabout the life of the section, as well as infor-mation about new developments in therespective sciences.

The Union is a member of importantinternational organisations, including theEuropean Mathematical Society, theEuropean Physics Society, and is also a rec-iprocity member of the AmericanMathematical Society.

Present ActivitiesDuring the 140 years of its existence, theUnion of Czech Mathematicians andPhysicists has dedicated an enormous effortto maintain and improve the teaching andresearch in mathematics and physics in alltypes of educational and scientific institu-tions. In the field of science, either inde-pendently or jointly with other institutionsof higher learning or research, it organisesnational and international conferences,symposia, seminars and various seasonalschools. It assists in the publication of text-books and monographs, closely cooperateswith the Publishing House Prometheus,Ltd., and takes part in the preparation ofnational basic research projects.

The Union publishes the journal Pokrokymatematiky, fyziky a astronomie (Advances inMathematics, Physics and Astronomy), spe-cialising on survey papers from contempo-

rary mathematics and physics, discussionsof pedagogical topics, and informationabout current activities of the Union.Among the journals published by theUnion we further find Matematika-fyzika-informatika (Mathematics-Physics-Inform-atics), aimed at the theory and practice ofteaching of the three subjects, Uèitel matem-atiky (Teacher of Mathematics), dedicatedto the didactic side of mathematical prob-lems, kolská fyzika (Physics in School),devoted to the teaching of physics, andfinally Èeskoslovenský Èasopis pro fyziku(Czechoslovak Physics Journal) andInformace MVS (Mathematical ResearchSection Newsletter), providing informationfor members of the respective sections.

In the field of education the Union sys-tematically studies the current state of theteaching of mathematics and physics andsuggests ideas for its improvement.

For more than 40 years the Union hasbeen organising various competitions forgifted young students at all levels in par-ticular, mathematics Olympiads, physicsOlympiads or the Student ResearchCompetition, traditionally attended ingreat numbers by the most brilliant stu-dents.

The Union awards a CommemorativeMedal to outstanding scientists, both fromthe Czech Republic and abroad, usually tothose who gained recognition for the devel-opment of mathematics or physics in theCzech Republic.

Most of the material presented in thisarticle was taken from [1]. Up-to-dateinformation was collected with the help ofseveral colleagues in particular, JiøíRákosník and Bøetislav Novák.

Reference1. L. Pátý and J. Veselý (eds.), Union ofCzechoslovak Mathematicians andPhysicists, JÈSMF, Polygraphia, branchPrometheus, Praha, 1984.

The author is an Assistant Professor at theFaculty of Mathematics and Physics of theCharles University in Prague. e-mail:pick@karlin.mff.cuni.cz Address: Department of Mathematical Analysis,Faculty of Mathematics and Physics, CharlesUniversity, Sokolovská 83, 186 75 Praha 8,Czech Republic.

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EMS March 2002 21

Two sides of theCommemorativeMedal, released

at the occasion ofthe Unions

125th anniver-sary in 1987.

Jaroslav Kurzweil

The main issue of the EMS Committee for Women andMathematics in the last two years has been to distribute in theEuropean mathematical community a questionnaire on thecareers of mathematicians and to try and analyse it. The ques-tionnaire (which follows) contains questions about progression inthe career (age, age of Ph.D., age of first permanent position,number of temporary positions, etc.), about family (job of parentsand of partner, number of children, etc.), about scientific activity(age when wrote best paper, possible gaps in mathematical pro-duction, and reasons for these gaps). Our aim was to checkwhether it is true, and in what measure, that there are differencesbetween the Curricula Vitae of men and women, and in particularwhether it is true that the scientific career of women is generallyslower, mainly because of family duties, especially children. Werethese hypotheses confirmed, we would have a basis to start someconcrete action, for instance against age limits in announcementsfor grants and prizes, which seem to be particularly discriminat-ing to women.

The questionnaire was distributed during the 3rd EuropeanCongress in Mathematics in Barcelona and its satellite meetingNew women in mathematics. It was also published in the EMSNewsletter and the newsletters of some other mathematical asso-ciations in Europe, and personally distributed by members of thecommittee. We have collected 109 answers, 52 by women and 57by men: not a big number. This shows, in our opinion, that unfor-tunately mathematicians have no wish to fill out questionnaires,and are not really very interested in the problem.

Almost one half of the respondents (45%) were from Norway:indeed the questionnaire was distributed in a capillary way inNorwegian mathematical departments, and the answers collectedby secretaries. So the picture of the situation in Norway is ratherfaithful. Of the other respondents, 15 were German, 13 Italian,but other countries were still less represented. There were a fewanswers from Russia and Romania, but none from other EastEuropean countries.

Here are some tables summarising the answers.

Age when Completed Ph.D. and when Wrote Best Paper

Many respondents obtained a permanent job before complet-ing their Ph.D.

On average, the female respondents are 6 years younger thanthe male respondents. This obviously affects the answers whenthe best paper was written: female age 32 and male age 36. Themean age of a Ph.D. is however the same for men and women.

Gaps in Mathematical Career46 respondents (26 female and 20 male) said that they had gaps

FEATURE

EMS March 200222

Mathematicians CarMathematicians Careers eers Analysis of a Questionnaire

Ina Kersten and Emilia Mezzetti

The questionnaireAre you male or female?How old are you?What is your nationality?How many children do you have?At what age did you complete your Ph.D.?How many countries have you studied/worked in?What is your mothers job? What is your fathers job?Do you have a permanent job?How many years after your PhD did you obtain your first permanent job?How many temporary mathematical jobs have you had?At what age did you write the paper of which you are most proud so far?Have you had any gaps in your mathematical career?

If so, how long were those gaps?In your opinion, what were the reasons for those gaps?

Comments:In some versions, the following questions were added:What is your partners job?Did you choose your place of residence motivated by your career or by thatof your partner?Did the problem of the residence play a role in your professional life?

in their mathematical career.

Frequency of reasons given by the respondents for gaps intheir mathematical career:

Number of respondents with a permanent job: 87/109 (female:35/52, male: 52/57)

How many years after your Ph.D. did you obtain your firstpermanent job?

The question of possible gaps in the mathematical career hadrather surprising answers: more women than men had gaps, butthe percentage is high also among men: 36%. For women themore frequent reason is family, but there are also academicduties or personal problems as depression or stress. Amongmen, all these reasons appear and moreover military service.

Partners jobAnswers to the question about job of partner and parents arerather interesting, but maybe not really related to our aim: themother is often a housewife, the father an engineer, or a school oruniversity professor, often in a scientific topic.

33 respondents (26 female and 7 male)

Mothers job

Fathers job

(*) mathematician in several cases

Other questions, for example the one about number of temporaryjobs, appear not relevant at all.

SUMMARYIn conclusion, we have to admit that the sample we have collectedis too small to allow us to draw any meaningful conclusion.

The results of this questionnaire have been illustrated duringthe 10th international meeting of European Women inMathematics (EWM) in Malta, 24-30 August 2001, where severalmembers of our committee were present.

An interesting and lively discussion followed. Particularly inter-esting was the contribution of Doris Janshen, a sociologist fromthe University of Essen. She gave us several suggestions. Weshould start again from the beginning, with a new well-thought-out questionnaire, taking into account as a basis the results of theprevious one. We should concentrate on a few countries only, andtry and collect a representative sample, as in Norway last time.Before distributing the new questionnaire, we should make somesamples, testing it on some selected EWM members, for example.This is what we plan to do.

For example, mathematicians of Eastern Europe did not showmuch interest in this kind of statistics, maybe because it is not dif-ficult to obtain a permanent job after a Ph.D. in these countries.A group in Ukraine, coordinated by Polina Agranovich, has nowprepared another series of questions and is currently distributingit in two universities in Kharkov. It is mainly devoted to under-standing the reasons for choosing mathematics and possible gapsin the career.

To conclude, we quote three recent articles that are somehowrelated to our work.

The first one is a report, written by A. Abele, H. Neunzert,R.Tobies and J. Krüsken, about the interdisciplinary project enti-tled Women in mathematics: factors determining mathematical careersfrom a gender comparative perspective, and supported by theVolkswagen Foundation. The article appeared in the Newsletterof the German Mathematical Society, DMV-Mitteilungen, 2-2001,p.8-16. It has recently been translated into English and willappear in the EMS Newsletter. It contains several very interestingdata and an analysis of the development of the situation of womenmathematicians in Germany. Among other things, it confirms thesometimes questioned fact that women and men have the samepotential capability of doing research. Women who succeed inconcluding Ph.D. studies in Germany obtain completely satisfac-tory results and get the same marks as their male fellows.

The second article is by Michèle Audin (Sur les étudiantes enmathématiques, Gazette des mathématiciens 87 (2001), 41-49,Newsletter of Société Mathématique de France). She analysed thepercentages of girls among first- and second-year students ofmathematics in her university in the 1990s and compared theresults of the exams. She concluded that girls choosing to studymathematics are much more motivated than boys and get betterresults. Once more, this convinces us that a stronger female pres-ence would be of great advantage to the mathematical communi-ty, that could enjoy big unexploited potentialities.

The last one is a recent article by Reuben Hersh, published in

FEATURE

EMS March 2002 23

The Mathematical Intelligencer: Mathematical menopause, or, ayoung mans game? (Math. Intelligencer 23 No.3 (2001), 52-60). Itdeals with the theme of the presumed incapacity of doingreasearch in mathematics after a certain age. On the basis ofresearch carried out among his friends and acquaintances (about65), the author concludes, among other things, that if it is truethat creativity decreases with age, then it is replaced by experienceand the capacity to coordinate the work of other people. So it ispossible to continue a good level of scientific activity after havingcrossed the famous threshold of 40 years, sometimes consideredas a limit age.

A short report on this questionnaire programme, by InaKersten and Emilia Mezzetti, will appear in the Proceedings of theEWM conference in Malta, to be published by World Scientific.Ina Kersten, Mathematisches Institut, Universität Göttingen,Bunsenstrasse 3-5, D-37073 Göttingen, Germany, e-mail: kersten@uni-math.gwdg.deEmilia Mezzetti, Dipartimento di Scienze Matematiche, Università degliStudi di Trieste, Via Valerio 12/1, 34127 Trieste, Italy, e-mail:mezzette@univ.trieste.it

Addendum to Obituary of Jacques-Louis Lions

(issue 42)In addition to the series that Jacques-Louis Lions edited, thereis one more: Studies in Mathematics and its Applications (with H. Fujita, H.B.Keller and G. Papanicolaou), 30 vols., North-Holland, 1976-2001. The authors contact details are:Philippe G. Ciarlet, Laboratoire dAnalyse Numérique,Université Pierre et Marie Curie, 4 Place Jussieu, F-75005PARIS, France. e-mail:pgc@ann.jussieu.frtel: (33)1.44.27.51.13; fax: (33)1.44.27.72.00

FEATURE

EMS March 200224

The The Human FHuman FrrontierontierScience PScience Prrogramogram

The Human Frontier Science Program promotes world-scaleresearch in the life sciences through Research Grants,Fellowships and Workshops.

The aim of the HFSP is to support basic research focused oncomplex mechanisms of living organisms; fields supportedrange from brain functions to biological functions at the mole-cular level. Particular emphasis is placed on bringing scientistsfrom fields such as physics, mathematics, chemistry, computerscience and engineering together with biologists, to open upnew approaches to understanding complex biological systems.

HFSP previously supported two scientific programmesfocused on neuroscience and molecular biology. With the dis-solving of boundaries separating traditional biological fields,and the need to involve disciplines outside biology in life sci-ence research, these separate programmes have been unifiedinto a single scientific program by the HFSP Board of Trustees.Henceforth, a single committee will review all grant applica-tions, while a second committee will review all long-term fel-lowship applications. Both committees are composed of leadinginternational scientists.

Research grants are awarded for projects that involve exten-sive collaboration among teams of scientists working in differ-ent countries. The emphasis is on novel collaborations thatbring together scientists from different disciplines. Fellowshipsare available to scientists who wish to work in foreign laborato-ries, with emphasis on individuals early in their careers.

Further information can be found on the web site:http://www.hfsp.org

Journal of the EuropeanMathematical Society

The next issue of JEMS (Vol. 4, No. 1) contains just one paperof 114 pages: Andreas Knauf, The n-centre problem of celestial mechanics forlarge energies

EurEuropean Wopean Women inomen inMaths WMaths Web-basedeb-based

Mentoring SchemeMentoring SchemeIn August the EU agreed to fund a project proposed by theorganisation European Women in Mathematics to provide web-based mentoring to women in mathematical sciences in Europe.Recent reports have highlighted (yet again) the lack of womenin higher positions in academia across scientific disciplines. TheEU is committed to improving the human potential acrossEurope, and in particular, to realising the talent of the femalepopulation, so this project has been given the go-ahead as astep towards encouraging women to progress in their mathe-matical science careers. The funding period for the EU schemeis 2 years and the scheme will be operated from Oxford BrookesUniversity in the UK.

Aim and scope of projectThe aim of the web-based mentoring scheme is to enable newwomen mathematical scientists (for example, graduate stu-dents, those considering graduate work, postdoctoral students)to find mentors amongst the mathematical science communitywho can advise them on academic issues and also on issues suchas how to apply for grants and how to prepare work for publi-cation. Mentors can also advise on broader gender-relatedissues faced by women in a mainly male-dominated environ-ment. Using the web to facilitate the mentoring scheme willenable women to form links with mentors across Europe.

Similar schemes are now starting up across the world forexample that run by the American Women in Mathematicsorganisation. We hope to link with them to provide mentors forEuropean women, and also to provide US mentors for thoseconsidering studying in the US. We hope that schemes of thisnature will contribute to the support network for women inmathematical sciences and encourage women to progress intheir mathematical science careers.

Further informationIf you are interested in joining the web-based mentoring projectas a mentor, or if you would like to use the scheme to find yourown mentor, please get in touch. We shall be actively seekingmentors soon and, when the project is up and running (laterthis year we hope), we will be inviting those who require men-tors to visit the site.

Contact: Dr Cathy Hobbs, School of Computing and MathematicalSciences, Oxford Brookes University, Gipsy Lane, Headington, OxfordOX3 0BP, UK. e-mail: cahobbs@brookes.ac.uk

Norway Introduces Major International Prize

There is no Nobel Prize for Mathematics, but nowThe Abel Prize has come into being

EMS NEWS

EMS March 2002 25

The European Mathematical Society hasbeen informed that the NorwegianGovernment has given a grant to covertravel and other expenses for a number ofyoung mathematicians from EasternEurope and the Former Soviet Union toattend the Abel Bicentennial Conferencein Oslo from 3-8 June 2002. The AbelBicentennial Conference will be theoccasion to introduce the newlyestablished Abel Prize to a wideinternational audience, and this GrantProgramme is intended as a part of thislaunch of the Prize.

The EMS has been asked to nominate15 young mathematicians for a travelgrant to attend the Abel BicentennialConference. The EMS ExecutiveCommittee has decided that its Committeefor the Support of Mathematicians fromEastern European Countries should makethese nominations.

Applicants are hereby invited from amongmathematicians from Eastern Europe and theFormer Soviet Union, who are not older than35 years.

Applications should include a short CVof the candidate (including contactdetails), brief information on theirresearch interests, a list of their mostimportant publications, and a letter ofrecommendation from an appropriateperson (such as a senior colleague orcollaborator).

Please send applications to the Chair ofthe Committee, preferably by electronicmail to the following address: , or by mailto Professor Andrzej Pelczar, InstytutMatematyki, Jagiellonian University,Reymonta 4, 30-059 Krakow, Poland),together with an electronic copyaddressed to Ms Tuulikki Makelienen inthe EMS Secretariat (makelain@kantti.helsinki.fi).

Applications should be received notlater than 20 April. Successful candidateswill be informed as soon as possible(preferably by electronic mail), andhopefully by 6 May.

Andrzej Pelczar

Niels Henrik Abel (1802-29) is one of theworlds most notable mathematicians. Heleft deep tracks behind him in manyfields. His points of view and hisapproaches were new and had decisivesignificance for the development ofmathematics as a science. Abel solvedproblems that mathematicians had beenstruggling with for centuries, and heposed approaches to problems with whichmathematicians are still working.

The year 2002 will be the 200thanniversary of the birth of Niels HenrikAbel, the leading man of science in thehistory of Norway. To mark this occasionthe Government of Norway, at thesuggestion of the Department ofMathematics at the University of Oslo hasundertaken to establish an Abel Prize in

GrantProgramme for

the AbelBicentennialConference

Oslo, 3-8 June 2002

Mathematics, following the model of theNobel prizes.

The Abel Prize has been well receivedinternationally, as attested to by TheInternational Mathematical Union(IMU):

The Executive Committee of IMU in itsrecent annual meeting, that took place at theInstitute for Advanced Study, in Princeton,considered the creation of the Abel Prize as themost important project in many years for thedevelopment of mathematics worldwide, in factas capable of greatly changing the scenariowithin a few years of its establishment. Ofcourse, the question of having an awardsimilar to the Nobel Prize for Mathematics is acentury old, and its lack is a perpetuallydiscussed feature of the scientific work of ourcommunity.

PROBLEM CORNER

Problem Corner: Back to Normality Paul Jainta

Croatian mathematics competitions at school Croatia is recovering from the troubles of the 1990s in particular, its educational set-up seems to have remained intact. eljko Hanj, a lecturer at the Department of Mathematics, University of Zagreb, gives us a brief insight behind the scenes of mathematical talent spotting in Croatia. Hanj was himself a contestant in the International Mathematical Olympia in 1977, and later acted as the leader of the Croatian IMO team in 1985 and from 1993 till 1999. Here is his account.

Our country has about 5 million inhabitants and an area of 56000 km2, so it is astonishing that mathematics competitions in this small area have survived for more than 40 years. Initially, they were aimed at students who attended secondary schools, but from 1965 on they have been expanded to primary schools too, including classes from ages 4 up to 8. The hierarchy of competitions that existed in Croatia unrevised since 1992 is as follows.

The first rather loose selection of mathematically gifted youngsters is carried out at school every January and February. The scene for this stage is thus provided by the intimate atmosphere of the educational institution before the competition jumps across school boundaries. Municipal competition Municipal competitions are organised in the larger towns with a total of about 8000 pupils in primary schools and approximately 2000 students in secondary schools. For the young participants these occasions represent stirring events, especially if they are involved for the first time. The municipal stage takes place at the beginning of March. The problems are chosen and prepared by separate subcommissions, responsible for entrants from primary school and secondary schools, respectively. These commissions are full of enthusiastic teachers and lecturers who pick all the questions with great care, and they grade the written papers and decide which students are permitted to enter the second stage. District decision Croatia is divided into 20 regions, with the capital Zagreb as a separate unit. The second stage includes all districts, and usually takes place in the middle of April. Again, each regional host town accommodates its own board to judge the results and pass them on to the national commission. The most successful competitors are awarded a price for the first time in the contest cycle. National round The members in the national board have the responsibility of deciding which contestants will be invited to attend the national competition. To this final stage only 7-formers from secondary schools and 8-formers from primary schools are admitted. The place of the final competition changes whenever possible. About 180 contestants and roughly 60 teachers and 40 members of the national contest board are travelling there separately. As a rule, this spectacle lasts for four days. On the second day when students are pondering on their solutions, lectures for the unoccupied teachers and coaches are given, split into subjects adequate for primary or secondary school curricula. Some topics sound good: the Euler and Fermat Theorem, the resolution of irrational equations, how can trigonometry help in solving algebraic problems? or an examination of a class of functions of the form fn(x) =cosn x + sinn x. The third day is usually reserved for a picnic with the entrants.

Soon after the results have been announced, we have to choose the team that will represent our country at the International Mathematics Olympiad. If the final round does not produce clarity in the line-up of this national team, further examinations follow to give additional information about the individual mathematical abilities of supplementary candidates. This screening is scheduled for the afternoon of the third day, and as a rule roughly 15-20 entrants have to undergo this extra treatment. Finally, the team is put together. In the evening of the same day the results are announced to the contestants. And in the morning of the day of departure, the assembled staff meet together to discuss how working with mathematically talented youngsters could be improved in future, or what topics the indigenous journals Matka, which is enjoyed by students at primary schools, and Matematičko- fizički, which attracts pupils from secondary schools, should pick up next. Regional contest Shortly after the final display is over, the time has come for students who visit fourth to sixth classes. They compete in regional contests that are organised in each of the four subregions of Croatia.

PROBLEM CORNER

Summer school for young mathematicians In summer, ever since 1972, a summer school is offered for young mathematics adepts, and a similar institution for primary school students opened its doors a few years ago. Meanwhile, about 100 young ace mathematicians amuse themselves with geometrical figures and numbers year by year. All these enumerated measures are under the auspices of the Croatian Mathematical society with support of the Ministry of Education and Sports. Our thanks go to eljko Hanj, who acted from 1991 onwards as Editor-in-Chief of the secondary school students journal Matematičk- fizički List and is thus a proficient reporter. The people of Croatia, especially the residents of Istria and Dalmatia, are traditionally growers of grapes or olives, or fishermen and seafarers. But in those regions, too, some ticklish maths problems are cultivated. Here is a sample. 134 Prove that there are at least 2000 triples of positive integers (a, b, c) such that a15 + b15 = c16.

(Municipal competition for secondary schools, 2000, II class) 135 Let a and b be real numbers that satisfy both a3 3ab2 = 44 and b3 3a2b = 8: determine a2 + b2.

(County competition for secondary school students 2000, I class) 136 A given rectangle with sides a and b is circumscribed by another rectangle of area m2: determine all

possible values of m. (County competition for secondary school students 1999, III class)

137 Given a right triangle with angles α and β, legs a and b and hypotenuse c. Prove the inequality: cos2(α β)/2 ≥ (2ab)/c2 . (County competition for secondary school students 2000, II class)

138 You have coins worth 1, 2, 5, 10, 20, 50 lipa and 1 kuna (= 100 lipa). Prove that if you can pay a bill for M lipa with N coins, then you can pay another bill for N kuna with M coins. (National competition 2000, I class)

139 A square is given in the plane with vertices T1 (1, 0), T2 (0, 1), T3 (1, 0), T4 (0, 1). For each n, let Tn+4 be the midpoint of the line segment TnTn+1. If the sequence of points Tn has a limit point, what are its coordinates? (County competition for secondary school students 1999, IV class)

Solutions to some earlier problems 122 Let A1A2A3A4A5A6A7 be a regular heptagon. Prove that 1/A1A2 = 1/A1A3 + 1/A1A4. Solution by Gerald A. Heuer, Concordia College, Moorhead (USA); also solved by Niels Bejlegaard, Copenhagen (Denmark); Pierre Bornsztein, Pontoise (France); Knut Dale, Telemark College, Bø (Norway); Pietro Fanciulli, Porto S. Stefano (Italy); J.N. Lillington, Dorchester (UK); Dr Z Reut, London (UK). Since A1A2 = 2r sin (π/7), A1A3 = 2r sin (2π/7) and A1A4 = 2r sin (3π/7), where r is the radius of the circumcircle, the equation to be proved is equivalent to 1/sin (π/7) = 1/sin (2π/7) + 1/sin (3π/7). (1) Adding the fractions on the right side of (1) and clearing of fractions, we obtain the equivalent equation sin (π/7) sin (3π/7) + sin (π/7) sin (2π/7) = sin (2π/7) sin (3π/7). (2) Using the formula sin a × sin b = ½[cos (a b) cos (a + b)], and simplifying, we find that (2) is equivalent to cos (2π/7) + cos (5π/7) = cos (3π/7) + cos (4π/7), which is obviously true because cos (π x) = cosx. 123 The sequence xn satisfies √(xn+2 + 2) ≤ xn ≤ 2 for all n ≥ 1. Find all possible values of x1986. Solution by Dr Z Reut, London. Assuming that the square root is positive, the sequence xn is positive. The system of inequalities: (xn+2 + 2)1/2 ≤ xn ≤ 2, gives by successive elimination: ((((xn+2m + 2)1/2 + 2)1/2 + + 2)1/2 ≤ xn ≤ 2, where there are m nested square roots on the left-hand side. If xn = 2, for all n, the double inequality is satisfied. Let us assume that the sequence xn is decreasing, that is: 0 < xn+2m < xn, and the difference is:

((((xn+2m + 2)1/2 + 2)1/2 + + 2)1/2 xn+2m < ((21/2 + 2)1/2 + + 2)1/2,

PROBLEM CORNER

which is less than the difference 2 xn+2m . It follows that 0 < xn+2m < 2 ((21/2 + 2)1/2 + + 2)1/2 = 0, on letting m go to infinity. Thus the only possible value of x1986, which is obtained for n = 2, m = 992, is 0. 124 Find the real numbers x1, x2, ,xn satisfying √(x1 −12) + 2 √(x2 −22) + + n √(xn− n2) = (x1 + x2 + + xn)/2. The following is a combination of similar solutions by Pierre Bornsztein, Pontoise, (France) and Dr Ranjeet Kaur Sehmi, Dept. of Applied Sciences, Punjab Engg. College, Chandigarh (India); also solved by Niels Bejlegaard, Knut Dale, , Gerald A. Heuer, J.N. Lillington and Dr Z Reut. Let √(xi i2) = yi for each i, so that xi = yi

2 + i2 for each i, and the given equation reduces to y1 + 2y2 + + nyn = (y1

2 + 12 + y22 + 22 + + yn

2 + n2)/2 or (y1

2 2y1 + 12) + (y22 4y2 + 22) + + (yn

2 2nyn + n2) = 0 or (y1 1)2 + (y2 2)2 + + (yn n)2 = 0, which is satisfied only when y1 = 1, y2 = 2, , yn = n. That is, x1 = 12 + 12 = 2×12, x2 = 22 + 22 = 2×22 , , xn = 2n2. 125 Prove that there is a perfect cube between n and 3n, for any integer n ≥ 10. Solution by Pierre Bornsztein; also solved by Niels Bejlegaard, Knut Dale, Gerald A. Heuer, Oren Kolman, Jerusalem (Israel), Dr Ranjeet Kaur Sehmi, J. N. Lillington, and Dr Z Reut. Suppose first that 10 ≤ n < 27; then n ≤ 33 ≤ 3n, trivially, and the result follows. If n ≥ 27, there exists a unique number x ≥ 3 such that x3 ≤ n < (x+1)3. To get the conclusion, it suffices to prove that (x+1)3 < 3n. Let n = x3 + k, where 0 ≤ k ≤ 3x2+3x. Then 3n = 3x3 + 3k = (x + 1)3 + 2x3 3x2 3x 1 + 3k. But one can easily see that the function f(x) = 2x3 3x2 3x 1 is increasing and positive for x ≥ 3. Thus f(x) > 0, for every integer x ≥ 3, and so 2x3 3x2 3x 1 + 3k > 3k > 0. It follows that n < (x+1)3 < 3n, as required. 126 Show that if √7 − m/n > 0 for the positive integers m, n, then √7 − m/n > 1/mn . Solution by J. N. Lillington, Dorchester; also solved by Niels Bejlegaard, Pierre Bornsztein, Knut Dale, Gerald A. Heuer, Oren Kolman and Dr Z Reut. If m = 1, then √7 − 1/n > 2 1/n ≥ 1 ≥ 1/n, and the result follows; so assume that m > 1. Consider the congruences of m ≡ 0, 1, 2, 3, 4, 5, 6 (mod 7); then m2 ≡ 0, 1, 4, 2, 2, 4, 1 (mod 7). Now given √7 − m/n > 0 ↔ 7n2 > m2, we have 7n2 ≠ m2 + 1, 7n2 ≠ m2 + 2 and 7n2 ≥ m2 + 3. Then 7m2n2 (m2 + 1)2 ≥ m2 (m2 + 3) (m2 + 1)2 = m2 1 > 0. This leads to √7 mn > m2 + 1, so that √7 > m/n + 1/mn or √7 − m/n > 1/mn. 127 Find all positive integers x, y, z satisfying 1+ 2x 3y = z2 . Solution by Knut Dale, Bø; also solved by Niels Bejlegaard, Pierre Bornsztein, Pietro Fanciulli J. N. Lillington, Erich N. Gulliver, Schwäbisch Hall (Germany), Dr Z Reut, London. Suppose that 1 + 2x 3y = z2; then z must be odd, z = 2k+1, and we get 2x-2 3y = k (k+1). With k = 1, 2, 3, we obtain the solutions (x, y, z) = (3, 0, 3), (3, 1, 5) and (4, 1, 7), but the first one is not possible because y > 0. The next value of k giving a solution is k = 8, leading to (x, y, z) = (5, 2, 7). Now assume that k ≥ 9 and let r = x2. Since k and k + 1 have no prime factors in common, we have to consider two cases: (1) k = 2r , k + 1 = 3y (r ≥ 4, y ≥ 3).

If y = 2t, then 2r = 3y 1 = (3t 1) (3t + 1). The only powers of 2 differing by 2 are 3t 1 = 2 and 3t + 1 = 4; so t = 1 and y = 2, contradicting y ≥ 3. If y = 2t + 1, then 2r = (2 + 1)2t+1 1 = 4a + 2(2t + 1), for some a, by the binomial theorem. But this is impossible, since r ≥ 4.

(2) k = 3y, k + 1 = 2r (r ≥ 4, y ≥ 2). If r = 2t, then 3y = 2r 1 = (2t 1) (2t + 1). The only powers of 3 differing by 2 are 2t 1 = 1 and 2t + 1 = 3; so t = 1 and r = 2, contradicting r ≥ 4. If r = 2t + 1, then 3y = 2r 1 = (3 1)2t+1 1 = 3b2, for some b, by the binomial theorem. But this is impossible, since y ≥ 2.

Please e-mail announcements of Europeanconferences, workshops and mathematical meetings ofinterest to EMS members, to k.a.s.quinn@open.ac.uk.Announcements should be written in a style similar tothose here, and sent as Microsoft Word files or as textfiles (but not as TeX input files). Space permitting,each announcement will appear in detail in the nextissue of the Newsletter to go to press, and thereafterwill be briefly noted in each new issue until the meetingtakes place, with a reference to the issue in which thedetailed announcement appeared.

1 April -30 June: Trimester on Algebraic Topology,Barcelona, Spain[For details, see EMS Newsletter 42]

29 April-12 July: Trimester on Financial Markets:Mathematical, Statistical and Economic Analysis,Pisa, Italy Scientific committee: W. Brock, D. Duffie, P.Embrechts, D. Farmer, H. Follmer Main visitors: K. Bach, M.M. Dacorogna, D. Duffie, J.D. Farmer, C. H. Hommes, J. Karatzas, Y. Kabanov, D.Madan, A. McNeil, T. Mikosch, M. Pagano, R.G.Payne, A.M. Rivlin, K. Singleton, N. Touzi Location: Centro di Ricerca Matematica E. De Giorgi,Scuola Normale Superiore, PisaInformation:web site: http://www.crm.sns.it

13-17: 34th Journées de Statistique, Brussels andLouvain-la-Neuve, BelgiumInformation: web site: www.stat.ucl.ac.be/JSBL2002[For details, see EMS Newsletter 41]

13-31: School and Conference on Probability Theory,Trieste, Italy Scope: this School will concentrate on three areas ofprobability: particle systems, combinatorics and randomenvironment. Different biological and physical systemscan be modelled in terms of interacting particle systemsand a study of some specific models is very rewarding.Scaling limits of large systems result in considerablesimplification of the description of the systems as theyevolve in time. The connection between probability andcombinatorics is undergoing a revolution at the moment.Issues of conformal invariance of certain two-dimensional models are just beginning to be understood.Percolation and random walks in a random environmentprovide examples of the complexities that can resultfrom being in a stationary but random environment,whose spatial fluctuations can cause strange things tohappenAim: the lecturers are researchers who have madesignificant contributions to the field. Their lectures willprovide an opportunity for the participants to learn first-hand about some of the far-reaching recentdevelopments in the fieldTopics: interacting particle systems, scaling limits ofparticle systems, dimers and geometry, conformallyinvariant processes in the plane, percolation, randomwalks in random environmentMain speakers: include L.R. Fontes (Brazil), R.Kenyon (France), C. Landim (Brazil), G. Lawler(U.S.A.), T. Liggett (U.S.A.), V. Sidoravicius (Brazil),A.-S. Sznitman (Switzerland)Programme: the first two weeks (13-24 May) will bedevoted to expository lectures on the topics listed above,while in the last week (27-31 May) there will be a high-

May 2002

April 2002

level conference, where current research and latestresults and developments in the field will be presentedby expertsOrganising committee: G. Lawler, C.M. Newman andS.R.S. Varadhan (all USA) Location: the Abdus Salam International Centre forTheoretical Physics, Strada Costiera 11, Trieste. Grants: a few financial grants are available forapplicants from, and working in, developing countriesonlyDeadline: already passedInformation: e-mail: smr1407@ictp.trieste.it web site: http://www.ictp.trieste.it/www_users/math/maths2002.html

15-17: Fourth International Conference on Advancesin Fluid Mechanics, Ghent, BelgiumInformation: web site: http://www.wessex.ac.uk/conferences/2002/afm02/index.html[For details, see EMS Newsletter 42]

19-26: Symmetry and Perturbation Theory(SPT2002), Cala Gonone, Sardinia, ItalyInformation: web site:http://web.tiscalinet.it/spt_spt/spt2002.html

22-24: Discrete Groups and Geometric Structures,with Applications (Crystallographic Groups andtheir Generalizations III), Kortrijk, BelgiumInformation: web site:http://www.kulak.ac.be/workshop[For details, see EMS Newsletter 42]

22-25: International Workshop on Visualization andMathematics 2002 Berlin-Dahlem, Germany Aim: to provide an active forum for mathematicians andcomputer graphics researchers on the fundamentalproblems of visualization techniques, on applications inmathematics and on mathematical concepts invisualization. It is the third symposium in a series ofworkshops bringing together mathematicians and expertsfrom computer graphicsTopics: visualization in differential geometry and partialdifferential equations, algorithmic representation ofmathematical structures, computational aspects oftopology, discrete geometry of meshes, compression oflarge and time-dependent geometric models, virtuallaboratories for mathematics and applications, on-linevisualization and computational web servicesKeynote speakers: Rida Farouki, Markus Gross, AlfioQuarteroni, Jurgen Richter-Gebert, Gabriel TaubinInvited Speakers: Phil Bowers, Mathieu Desbrun,Gerald Farin, Joel Hass, Beau Janzen, Chris Johnson,Ravi Malladi, Tom Wickham-JonesConference chairs: Christian Hege and Konrad PolthierProgramme committee: Helmut Alt, James Arvo,Chandrajit Bajaj, Thomas Banchoff, Ken Brakke, PeterDeuflhard, Thomas Ertl, Gerald Farin, George Francis,Hans Hagen, David Hoffman, Chris Johnson, MichaelJoswig, Leif Kobbelt, Heinrich Muller, Gregory Nielson,Ulrich Pinkall, Helmut Pottmann, Martin Rumpf,Dietmar Saupe, Hans-Peter Seidel, John Sullivan,Nobuki Takayama, Ross Whitaker, Luiz Velho, Jarkevan Wijk, Gunter Ziegler Organisers: Sonderforschungsbereich DifferentialGeometry and Quantum Physics (Sfb 288) at theTechnische Universität in Berlin, Department ofScientific Visualization at the Konrad-Zuse-Zentrum furInformationstechnik Berlin (ZIB) Format: keynote lectures, invited talks and contributedpresentations. The time for keynote lectures, invitedtalks and contributed talks will be 50, 40, and 30minutes (respectively), including discussions. There willbe possibilities for software demonstrationsCall for papers: interested contributors are asked to

submit a full paper for review by the programmecommittee. Articles by keynote lecturers, invitedspeakers and contributors will be published by Springer-Verlag in the book series Mathematics andVisualization. For preparation of papers please use theLaTeX templates for multi-authored books availablefrom http://www.springer.de/math/authors/b-tex.html.For review papers should be submitted on-line, using thepaper submission form at the workshop website.Participants will receive a volume of abstractsSponsor: Deutsche Forschungsgemeinschaft (DFG) Location: Harnack-Haus in Berlin-DahlemDeadlines: for submission of papers, 10 March; for finalpapers, 30 April; for on-line registration, 30 AprilInformation: e-mail: vismath@math.tu-berlin.deweb site: http://www.math.tu-berlin.de/vismath

25-3 June: XXII International Seminar on StabilityProblems for Stochastic Models (SPSM) andSeminar on Statistical Data Analysis (SDA), Varna,BulgariaInformation: web site: http://stabil.fmi.uni-sofia.bg[For details, see EMS Newsletter 41]

27-29: Spring School on Frobenius Manifolds inMathematical Physics, Enschede, The NetherlandsInformation: e-mail: nijpjes@sci.kun.nl

27-29: Frobenius Manifolds in Mathematical Physics,The NetherlandsLocation: University of Twente, Enschede Organising committee: G. Heckman, G. Helminck, R.Martini, P. Kersten, J. van de Leur, E. Looijenga, J.Stienstra (all from the Netherlands)Local organising committee: G. Helminck and P.Kersten Sponsors: Mathematical Research Institute (MRI),NWO (Netherlands Organization for ScientificResearch), University of Twente, Faculty ofMathematical Sciences of the University of Twente(Netherlands), FOM (Foundation for FundamentalResearch, the Netherlands) Speakers: R. Dijkgraaf (Netherlands), B. Dubrovin(Trieste), T. Eguchi (Tokyo), C. Hertling (Bonn), A.Morozov (Moscow), I. Krasilshchik (Moscow), S.M.Natanzon (Moscow), L. Takhtajan (New York)Information: e-mail: p.h.m.kersten@math.utwente.nl(programme and registration),d.dalenoord@math.utwente.nl (local managing director)web site: http://www.math.utwente.nl/fa/springschool/

27-31: 6th Congress of SIMAI (The Italian Societyfor Applied and Industrial Mathematics), Chia,Sardinia, ItalyInformation: web site: http://www.iac.rm.cnr.it/simai(click on simai 2002)[For details, see EMS Newsletter 42]

28-31: 2nd International Conference on AdvancedComputational Methods in Engineering (ACOMEN2002), Liège, BelgiumInformation: web site: http://cage.rug.ac.be/~acomen[For details, see EMS Newsletter 42]

30-2 June: Conference in Honour of StevenKleimans 60th Birthday, Oslo, Norway Theme: algebraic geometry and commutative algebra Topics: motivic cohomology, moduli problems,intersection theory, enumerative geometry Speakers: Henning H. Andersen (Aarhus), Larry Breen(Paris 13), Herb Clemens (Utah), Susan Colley(Oberlin), Dan Edidin (Missouri), Eduardo Esteves(IMPA/MIT), Dan Grayson (Illinois), Tony Iarrobino(Northeastern), Bernard Teissier (Paris 7), IsraelVainsencher (UFPE), Ravi Vakil (Stanford), AngeloVistoli (Bologna) Organising committee: Susan Colley (Oberlin), DanEdidin (Missouri), Dan Grayson (Illinois), Ragni Piene(Oslo) Sponsors: MIT Math. Dept., Norwegian Academy ofSciences and Letters, Centre for Advanced Study (Oslo),Research Council of Norway, NORDAG (NorFA)Location: Norwegian Academy of Science and Letters,Drammensveien 78, Oslo, Norway Information: e-mail: ragnip@math.uio.no web site: http://www.math.uiuc.edu/~dan/Kleiman60/

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FForthcoming conferorthcoming conferencesencesCompiled by Kathleen Quinn

3-7: Conference dedicated to the 90th anniversary ofB. V. Gnedenko, Kyiv, Ukraine Theme: probability theory and its applications Aim: the focus will be on topics close to the wide rangeof scientific interests of B.V. Gnedenko. The aim is two-fold: first, to highlight the contributions of B.V.Gnedenko in probability theory and its applications,history of mathematics, problems of education, and,second, to present the developments of his ideas as wellas the current trends in the theory of probability andrelated fieldsTopics: limit theorems for independent randomvariables; quality control, reliability theory, queueingtheory; extremal statistics, random sums; parametricstatistics, test of hypotheses; asymptotics of stableprocesses; statistical change point analysis; issues ineducation; limit theorems for random fields; stochasticsand mathematical physics; statistical methods withapplications to insurance and finance; probabilisticnumber theory; discrete probabilistic models; stochasticanalysis Programme committee: A.V. Skorokhod (USA),Yu.V. Kozachenko (Ukraine), A.I. Martikainen (Russia),V.V. Petrov (Russia), Yu.K. Belyaev (Sweden), I.N.Kovalenko (Ukraine), A.V. Ivanov (Ukraine), Yu.N.Linkov (Ukraine), J. Steinebach (Germany), N.Kh.Rozov (Russia), D. Vere-Jones (New Zealand), M.I.Yadrenko (Ukraine), A.V. Bulinskii (Russia), N.N.Leonenko (UK), S. Albeverio (Germany), Yu.M.Berezanskii (Ukraine), Yu.G. Kondratiev(Ukraine),Yu.S. Mishura (Ukraine), A.G. Kukush (Ukraine), K.-H.Indlekofer (Germany), I. Katai (Hungary) Organising committee: V.S. Korolyuk (Ukraine) andYu.V. Prokhorov (Russia) (co-Chairs), O.D. Borysenko(Ukraine), V.V. Buldygin (Ukraine), S.S. Demidov(Russia), D.B. Gnedenko (Russia), I.A. Ibragimov(Russia), V.I. Khokhlov (Russia), O.I. Klesov (Ukraine),Yu.G. Kondratiev (Ukraine), Yu.V. Kozachenko(Ukraine), Yu.S. Mishura (Ukraine), M.O. Perestyuk(Ukraine), N.I. Portenko (Ukraine), Yu.A. Rozanov(Italy), A.M. Samoilenko (Ukraine), V.V. Sazonov(Russia), B.A. Sevastyanov (Russia), A.N.Shiryaev(Russia), Ya.G. Sinai (Russia), M.I. Skil(Ukraine), V.V. Skopenko (Ukraine), A.V. Skorokhod(USA), M.I. Yadrenko (Ukraine), O.K. Zakusylo(Ukraine), M.Z Zgurovskii (Ukraine), V.M. Zolotarev(Russia) Sponsors: Ministry of Education and Science ofUkraine, Center for Science and Methodology of HigherEducation, Kyiv National Taras Shevchenko University,National Technical University of Ukraine (KPI),National Pedagogical Dragomanov University, LvivFranko State University, Institute for Mathematics,National Academy of Science of Ukraine,Mathematica Foundation, Moscow State MikhailLomonosov University, Steklov Institute forMathematics, Russian Academy of Science, BernoulliSociety, INTAS Conference Abstracts: abstracts should be sent toabstract@tbimc.freenet.kiev, typeset for AMS TeX inamsppt style. If you are not familiar with AMS TeX,please copy the template file athttp://ln.com.ua/~tbimc/gnedenko/ Proceedings: papers for the Proceedings should be sentto abstract@tbimc.freenet.kiev.ua or submitted uponarrival, typeset for AMS TeX in amsppt styleLocation: Kyiv National Taras Shevchenko University(Volodymyrska, 60), Kyiv, Ukraine Grants: restricted number of grants for participantsfrom the former Soviet Union and youngmathematiciansDeadlines: for requests for a letter of invitation, 31March; for abstracts, 30 April; for requests for a hotelreservation, 10 MayInformation: e-mail: oleg@tbimc.freenet.kiev.uafax: +38-044-513-84-07web site: http://ln.com.ua/~tbimc/gnedenko/

3-8: Abel Bicentennial Conference 2002, Oslo,NorwayLocation: University of OsloTheme: 2002 marks the bicentennial of the birth ofNiels Henrik Abel, 1802-29. The conference will

June 2002 present an overview of the mathematical heritage ofAbel and, based upon this heritage, identify newmathematical trends for the 21st centuryTopics: there will be sections on the history ofmathematics, algebraic geometry, complex analysis,differential equations, non-commutative geometryInvited speakers: Michel van den Bergh, FabrizioCatanese, Ciro Ciliberto, Herbert Clemens, AlainConnes, Gerd Faltings, John Erik Fornæss, Günter Frei,William Fulton, Mark Green, Phillip Griffiths, GuenadiHenkin, Christian Houzel, Steven Kleiman, Igor M.Krichever, Hendrik W. Lenstra, Mark Melnikov, RomanNovikov, Norbert Schappacher, Atle Selberg, Yum-Tung Siu, Dennis Sullivan Support: a few grants are available for youngmathematicians, including participants from third worldcountries. Grants will be approximately 1000 euro eachand should cover travel expenses and lodging Sponsors: International Mathematical Union, TheNorwegian Academy of Science and Letters, Ministry ofEducation, Research and Church Affairs, TheNorwegian Agency for Development Cooperation(NORAD)Scientific committee: Michael Artin, Gerd Faltings,Phillip A. Griffiths, Gennadi Henkin, Christian Houzel,Olav Arnfinn Laudal, Jacob Palis Information: web site:http://www.math.uio.no/abel/conference/index.html

3-8: Algebra Conference Venezia 2002, Venice,ItalyTopics: abelian groups, algebras and theirrepresentations, commutative rings, module theory, ringtheory, topological algebraic structuresMain speakers: S. Bazzoni (Italy), A. Facchini (Italy),R. Farnsteiner (Germany), R. Gilmer (USA), R. Goebel (Germany), W. Heinzer(USA), H. Krause (Germany), K. Kunen (USA), I.Reiten (Norway), J. Trlifaj (Czech Republic), C.Vinsonhaler (USA), R. Wiegand (USA) Plenary speakers: R. Colpi (Italy), D. Herbera (Spain),S. Kasjan (Poland), B. Olberding (USA), D.Shakhmatov (Japan), L. Struengmann (Germany)Scientific committee: D. Dikranjan (Italy), A. Facchini(Italy), M. Fontana (Italy), L. Fuchs (USA), K. Fuller(USA), R. Göbel (Germany), W. Heinzer (USA), C.Ringel (Germany), D. Simson (Poland)Organising committee: F. Barioli, S. Bazzoni,, R.Colpi, S. Gabelli, E. Gregorio, C. Metelli, L. Salce, F.Stumbo, A. Tonolo, P. Zanardo (Italy)Site: Venice International University, Island of SanServolo, VeniceDeadlines: registration and abstracts, 31 MarchProceedings: to be published by Marcel Dekker, Inc.Information: e-mail: tonolo@math.unipd.itweb site: http://dm.unife.it/~venezia/

3-9: BIOCOMP2002, Vietri sul Mare, Italy Theme: mathematical biology and biocomputation Programme: invited lectures, selected contributedpapers and round-table discussionsAim: to bring together specialists of various fields tofocus on the relevant problems of mathematical biologyand biocomputation at the beginning of the thirdmillennium Topics: biomechanics and molecular motors; patternformation; spatial and non-linear dynamics in populationbiology and ecology; coding, computations andstochasticity in neurobiology and other excitable media;biocomputing, bioinformatics and gene networksProgramme committee: S. Amari (Japan), J.J. Collins(USA), P. Cull (USA), I. Eshel (Israel), M. Iannelli(Italy), P. Lánský (Czech Republic), S.A. Levin (USA),Z. Ma (China), M. Mimura (Japan), R. Moreno Diaz Sr.(Spain), K. Pakdaman (France), L. Peliti (Italy), F.Pichler (Austria), S. Sato (Japan), J.P. Segundo (USA),C.E. Smith (USA), A. Tesei (Italy), H.C. Tuckwell(Australia), F. Ventriglia (Italy), G. Vidossich (Italy), T.Yanagida (Japan) Organising committee: Luigi M. Ricciardi, Chair(http://cds.unina.it/~ricciard/), U. Amato, W. Balzano, A.Buonocore, S. Chillemi, A. Dattolo, A. Di Crescenzo, E.Di Nardo, P. Festa, V. Giorno, M. Longobardi, K.Nakagawa, A.G. Nobile, E. Pirozzi, S. Rinaldi, L.Sacerdote Sponsors: University of Napoli Federico II, University

of Osaka, Tel Aviv University Location: Vietri sul Mare (near Naples) Deadlines: abstracts, already passed; registrations, stillopen Information: web site: http://biocomp.unina.it

4-13: 3rd Linear Algebra Workshop BLED 2002,Bled, SloveniaInformation: web site:http://www.ijp.si/ftp/pub/STOp/law/[For details, see EMS Newsletter 41]

5-8: Free Boundary Problems, Trento, Italy Topics: free boundary problems, phase transitions, fluidfiltration, ferromagnetism, mechanics, materials science,biomathematics, image processing, computationalmethodsMain speakers: L. Ambrosio, G. Bertotti, Z. Chen, P.Degond, E. Di Benedetto, W. Dreyer, C.J. van Duijn,M.E. Glicksman, N. Kenmochi, R. Kohn, S. Mueller, J.-M. Morel, R.H. Nochetto, F. Otto, O. Penrose, E.Presutti, A. Quarteroni, F. Reitich, A. Schmidt, M.Soner, V. Starovoitov, J.J.L. VelazquezFocus sessions: free boundary problems in polymerscience, image processing, grain boundary motion,optimal design for free boundary problems, numericalaspects of free boundary problems, free boundaryproblems in biomathematics, modelling of crystalgrowth, transitions with anisotropyPoster session: open to contributions by all participants Programme committee: P. Colli , G. Dziuk, A. Fasano,M. Fremond, A. Friedman, S. Luckhaus, K.-H.Hoffmann, M. Niezgodka, J. Ockendon, M. Primicerio,J.-F. Rodrigues, J. Sprekels, C. Verdi, A. Visintin Organising committee: P. Colli, G. Dziuk, A. Fasano,K.-H. Hoffmann, J. Sprekels, C. Verdi, A. Visintin(local organiser) Sponsors: University of Firenze, University of Freiburgi. Br., University of Milano, University of Pavia,University of Trento, C.A.E.S.A.R. Institut Bonn,W.I.A.S. Berlin, Deutsche Forschungsgemeinschaft,G.N.A.M.P.A., G.N.C.S., G.N.F.M. of I.N.d.A.M.,Project Free Boundary Problems of M.I.U.R., ProjectScientific Computing: of M.I.U.R., ProjectSymmetries, Geometric Structures, of M.I.U.R. Venue: Centro S. Chiara, via S. Croce 67, Trento Grants: for participants from weak currency countries,or born after 1 January 1967Information: e-mail: P. Colli pier@dimat.unipv.it web site: http://fbp2002.unitn.it/

5-9: Conference in Honour of Hans Wallin, Umea,SwedenInformation: web site:http://www.math.umu.se/aktuellt/HWkonferens.htm[For details, see EMS Newsletter 41]

6-8: Zero Dimensional Schemes and Related Topics,Acireale, Sicily, Italy [in honour of Tony Geramita on the occasion of his 60thbirthday]Theme: algebraic geometry and commutative algebra Main speakers: Karen Chandler (Notre Dame), LucaChiantini (Siena), Aldo Conca (Genova), AlessandroGimigliano (Bologna), Martin Kreuzer (Regensburg),Tony Iarrabino (Northeastern), Rosa María Miró-Roig(Barcelona), Uwe Nagel (Paderborn), Leslie Roberts(Queens), Rosario Strano (Catania), Bernd Ulrich(Purdue)Organising committee: Eddy Campbell (Queens),Brian Harbourne (Nebraska), Juan Migliore (NotreDame), Ferruccio Orecchia (Napoli), Alfio Ragusa(Catania), Lorenzo Robbiano (Genova) Grants: limited funding available for young researchersRelated conferences: the AMS-UMI meeting in Pisa,12-16 June (http://www.dm.unipi.it/~meet2002/) hasseveral special sessions in commutative algebra andalgebraic geometry; Current Trends in CommutativeAlgebra, Levico, 17-21 June, (http://www.dima.unige.it/~rossim/Levico.html) is also of interestInformation: web site:http://cocoa.dima.unige.it/conference/acireale/first.html

6-15: Fourth International Conference on Geometry,Integrability and Quantization, Varna, BulgariaInformation: web site:

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http://www.bio21.bas.bg/conference/[For details, see EMS Newsletter 42]

10-14: Homology Theories, Representations andHopf Algebras, Luminy, FranceTheme: homological algebra, representation theoryTopics: Green functors, tilting objects, invarianceproperties of automorphism groups, Hochschildcohomology, Hopf algebrasProgramme: short courses (each of three 45-minutelectures), also conference talksCourse speakers: Serge Bouc Paris 7 (France), DieterHappel Chemnitz (Germany), Manuel Saorin Murcia(Spain) Conference speakers: N. Andruskiewitsch (Argentina),A. Bruguieres (France), F. Coelho (Brazil), S. Dourlens(France), F. Dumas (France), M. Farinati (Argentina), D.Guin (France), M. Karoubi (France), C. Kassel (toconfirm) (France), T. Lambre (to confirm) (France), P.Malbos (France), E. Marcos (Brazil), S. Natale(Argentina), F. Patras (France), E. Reynaud (France), M.Rosso (France), C. Strametz (France), M. SuarezAlvarez (Argentina), R. Taillefer (France), L. Unger(Germany), M. Vigue-Poirrier (France), A.Zimmermann (France)Languages: English, French Organising committee: Claude Cibils (France), MariaJulia Redondo (Argentina), Andrea Solotar (Argentina)Sponsors: CIRM (France), Université de Montpellier 2,Université de Paris 7, TMR network K-Theory, LinearAlgebraic Groups and Related Subjects, Ambassade deFrance in UKLocation: CIRM, Luminy, Marseille (http://cirm.univ-mrs.fr) Fees: no registration fee; cost of lodging at CIRM isaround 45 euros a day, including mealsDeadlines: for registration, 5 May (write tolacan@math.univ-montp2.fr) Information: e-mail: claude.cibils@math.univ-montp2.fr, solotar@math.univ-montp2.fr,asolotar@dm.uba.ar web site: gauss.math.univ-montp2.fr/~cibils/CIRM2002

10-16: Aarhus Topology 2002, Aarhus, DenmarkInformation: web site: http://www.imf.au.dk/AT2002/[For details, see EMS Newsletter 41]

11-13: Third International Symposium on RemoteSensing of Urban Areas, Istanbul, TurkeyInformation: web site:http://www.ins.itu.edu.tr/deryamaktav[For details, see EMS Newsletter 42]

12-16: 2002 WSEAS International Conferences onSignal Processing, Robotics And Automation (ISPRA02); Microwaves, Antennas & Radar Systems(IMARS 02); Electronics & Hardware Systems(IEHS 02), Cadiz, Spain Information: web site:http://www.wseas.org/conferences/2002/spain

16-23: Second Russian-German Geometry Meeting,St Petersburg, Russia[dedicated to the 90th anniversary of A.D. Alexandrov(1912-99)]Topics: differential geometry, non-linear differentialequations in geometry, geometric analysis, singularspaces, foundations of geometry, applications ofgeometry to mathematical physics and algebraOrganisers: W. Ballmann (Bonn), Yu. Burago (StPetersburg), Yu.G. Reshetnyak (Novosibirsk)Co-organisers: S.V. Buyalo (St Petersburg), D. Schueth(Bonn), I.A. Taimanov (Novosibirsk)Location: Euler International Mathematical Institute,Pesochnaya nab. 10, St Petersburg 197022Deadline: for registration, 15 AprilInformation: e-mail: geo2@imi.ras.ru,geometry@math.uni-bonn.de, geometry@math.nsc.ru web site: http://www.pdmi.ras.ru/EIMI/2002/geo2/

17-19: 24th World Conference on Boundary ElementMethods incorporating Meshless Solutions SeminarSintra, PortugalInformation: web site: http://www[For details, see EMS Newsletter 42]

17-21: Advanced School and Workshop onMathematical and Computational Modeling ofBiological Systems, Lisboa, PortugalTheme: mathematical and computational modeling ofbiological systemsAim and Format: to provide an updated overview oftypical models and tools used in mathematical andcomputational studies of biological tissues, organs andsystems. The event has two components: AdvancedCourse and Research WorkshopTheme: mathematics and biology, with specialemphasis on modelling tissues, organs and systems ofthe human bodyTopics: mechanics of soft tissues, mechano-electricalfunction of the heart, thermo-chemo electro-mechanicsof porous media, skeletal muscles and neuromuscularcontrol, control and mechanics of human movementsystems, physiological fluid mechanicsMain speakers: Gerhard Holzapfel (Austria), PeterHunter (New Zealand), J. Huyghe (Netherlands), J. vanLeewen, (Netherlands), Clyde Martin (USA), Prof.Oliver Jensen (UK)Programme: 18 hours of Course lectures; 9 hours ofWorkshop paper presentations and discussionsCall for papers: two-page abstracts containing theauthors name, affiliation, address, and e-mail can besent by e-mail (text, word, pdf, or ps format) or by faxOrganising committee: J.A.C. Martins, IST, Portugal,E.B. Pires, IST, PortugalMain sponsor: this event is part of the Thematic Termon Mathematics and Biology, sponsored by CIM (CentroInternacional de Matemática), a member of ERCOM -European Research Centres on MathematicsOther sponsors: Instituto de Engenharia de Estruturas,Territorio e Construção (ICIST), Fundação CalousteGulbenkian Fundação para a Ciência e a Tecnologia(FCT) Proceedings: to be published Location: Congress Centre of Instituto Superior TécnicoBuilding of the Departamento de Engenharia Civil eArquitectura Instituto Superior Técnico, Lisboa, PortugalGrants: 30 euro discount for studentsNotes: class notes will be provided to participantsDeadlines: for receipt of abstracts, 15 March Secretariat and Address: Helena Romão, ICIST, Dep.Eng. Civil e Arquitectura, Instituto, Superior Técnico,Av. Rovisco Pais, 1, 1049-001 Lisboa, Portugal, phone:(+351) 21 841 8401, fax: (+351) 21 849 7650 Information: e-mail: bio.systems@civil.ist.utl.ptweb site: http://www.civil.ist.utl.pt/bio.systems

17-21: Seventh international conference on p-adicfunctional analysis, Nijmegen, The Netherlands [analysis in and over valued fields other than R or C]Scientific committee: W. Schikhof (Netherlands), A.Escassut (France), C. Perez-Garcia (Spain) Programme: each participant is asked to contribute ahalf-hour lecture on recent research, in EnglishAbstracts: to Ms. W. van de Sluis (local manager), e-mail: willy@sci.kun.nl Proceedings: we intend that these will be published.Participants are asked to deliver a manuscript at the startof the conference: more details will be available laterSponsors: Mathematical Research Institute (MRI)(Netherlands), NWO (Netherlands Organization forScientific Research) (Netherlands), Subfaculty ofMathematics, University of Nijmegen (Netherlands) Deadlines: for abstracts, 1 May Information: e-mail: schikhof@sci.kun.nlweb site: http://www.sci.kun.nl/math/p-adic2002

17-21: Stochastic Inequalities and their Applications,Barcelona, Catalonia Aim: the topics to be covered belong to different areasof probability, statistics and analysis, and therefore theconference will provide a unique opportunity forexchange of ideas occurring in different fields and forinterdisciplinary contact and collaborationTopics: to include concentration and deviationinequalities for various types of processes usingisoperimetry, differential inequalities and informationinequalities, other exponential and moment inequalitiesfor sums of independent or weakly dependent randomvectors and related variables, inequalities in MalliavinCalculus, geometric inequalities for log-concaveprobability measures, particularly the Gaussian

correlation inequality, martingale and decouplinginequalities.Programme: plenary lectures, invited and contributedhalf-hour lectures, and problem and discussion sessionsMain speakers: Luis Caffarelli (Austin, USA), NicolaiKrylov (St Paul/Minneapolis, USA), Rafal Latalà(Warsaw, Poland), Michel Ledoux (Toulouse, France),Gàbor Lugosi, Barcelona, Catalonia), Pascal Massart(Orsay, France), Colin McDiarmid (Oxford, UK), PhilipProtter (Ithaca, USA), Emmanuel Rio (Versailles,France), Ofer Zeitouni (Haifa, Israel)Scientific programme committee: Evarist Giné (Storrs,USA), David Nualart (Barcelona, Catalonia), ChristianHoudré (Atlanta, USA)Local organising committee: David Nualart, FredericUtzet, Arturo Kohatsu, Maria JolisSponsors: Centre de Recerca Matemàtica, EuropeanCommission, Ministerio de Ciencia y Teconología(Spanish Government) and Bernoulli SocietyLocation: Centre de Recerca Matemàtica, UniversitatAutònoma de Barcelona, Science Building 08193,Bellaterra, Spain Deadlines: application for financial support, 5 April;registration and payment, 30 April Information: Secretary of the conference, Consol Roca,Centre de Recerca Matemàtica, Apartat 50, 08193Bellaterra, Catalonia, Spain; phone: 34-93-5811081. e-mail: crm@crm.es, web site:http://www.crm.es(activities)

17-21: XVth Householder Symposium on NumericalLinear Algebra, Peebles, ScotlandInformation: web site:http://www.maths.strath.ac.uk/~matrix/[For details, see EMS Newsletter 42]

17-22: School on Population Dynamics, Bêdlewo,PolandInformation: web site:http://www.math.us.edu.pl/cmmpd/[For details, see EMS Newsletter 42]

18-22: The Barcelona Conference on StochasticInequalities and their Applications(EuroConference), Bellaterra, Barcelona, SpainInformation: web site: http://www.crm.es/stochineq

18-23: Advanced School and Workshop on BoneMechanics: Mathematical and Mechanical Modelsfor Analysis and Synthesis, Lisbon, Portugal Main speakers: Martin P. Bendsoe (Denmark), AndrejCherkaev (USA), Stephen C. Cowin (USA), ManuelDoblaré (Spain), Rik Huiskes (Netherlands), HarrieWeinans (Netherlands), José M. Guedes (Portugal),Helder Rodrigues (Portugal) Organising committee: H. Rodrigues (Portugal), J.Guedes (Portugal) Proceedings: to be published Location: Instituto Superior Tecnico, Av. Rovisco Pais,Lisboa, PortugalInformation: e-mail: Bone.Mechanics@dem.ist.utl.pt web site: http://www.dem.ist.utl.pt/~bonemec

19-21: EUROMECH Colloquium 437: Identificationand Updating Methods of Mechanical Structures,Prague, Czech RepublicLocation: Institute of Thermomechanics, CzechAcademy of Sciences Theme: mathematical modelling of mechanicalstructuresTopics: parametric identification in frequency and timedomain, curve fitting of transfer functions, identificationof vibrating systems with small non-linearity, spectraland modal sensitivity, updating methods of finiteelement models, tuning and vibro-diagnostics ofmechanical structures, robustness of model-baseddecisions with respect to uncertainties Main speakers: G. Lallement (France), J. Piranda(France), M. Balda (Czech Republic), E. Hahn(Australia) Call for papers: participants are invited to contributepapers on the above topics. Oral presentation should bein English (25 minutes including discussion).Contributors should submit, as an attached file via e-mail to the e-mail conference address: ec437@it.cas.czor euromech.437@it.cas.cz, a one-page extended

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abstract of their proposed paper including its title,authors name, affiliation, full mail address and e-mailaddress. The extended abstracts will be reviewed by theScientific Committee; authors will be notified aboutacceptance by the end of April 2002. All acceptedpapers will be published in the Book of Abstracts of theEUROMECH Colloquium 437. The proceedings willbe available for delegates attending the Colloquium.Selected papers from the Colloquium will berecommended for the publication in internationaljournals for theoretical and applied mechanicsPreliminary scientific committee: Miroslav Balda(Czech Academy of Sciences), Vasyl ChekurinPidstryhach (National Academy of Sciences, Ukraine),Ivan Dobias (Czech Academy of Sciences), JaromirHoracek (Czech Academy of Sciences), Jean Piranda(University Franche Comte), Ladislav Pust (CzechAcademy of Sciences), Alexandru Valentin Radulescu(University Politehnica, Bucharest), Gu Zhengqi (HunanUniversity, P.R. China) Chairs: Gerard Lallement AML RC, University FrancheComte, Besancon, France, Jan Kozanek, Institute ofThermomechanics, Czech Academy of Sciences Location: Institute of Thermomechanics, CzechAcademy of Sciences, Dolejskova 5, 182 00 Prague 8,Czech Republic Grants: some reduction of fees for young participants Deadlines: for submission of extended abstracts, 29March (acceptance by 30 April); for payment, 10 May Information: e-mail: ec437@it.cas.czeuromech.437@it.cas.cz fax: +420-2-86584695, web: http://www.it.cas.cz/ec-437/

21-26: Symmetries and Integrability of DifferenceEquations: EuroConference on Discrete PainlevéEquations and the Solvability of DifferenceEquations, Giens (near Toulon), France Topics: to include analytic and algebraic aspects ofdifference equations, difference Galois theory, thePainlevé property and singularity analysis, growth andbranching phenomena in rational mappings, differenceanalogues of the Painlevé equations, isomonodromicdeformation theory, asymptotics of orthogonalpolynomials, symmetries of difference equations,applications to numerical analysisMain speakers: Mark J. Ablowitz (Boulder, USA);Alexander Its (Indianapolis, USA); Reinout Quispel(Bundoora, Australia); Claude Brezinski (Lille, France);Nalini Joshi (Adelaide, Australia); Alfred Ramani (Paris,France); Peter Clarkson (Canterbury, UK); MartinKruskal (Rutgers, USA); Konstantin Rerikh (Dubna,Rumania); Robert Conte (Saclay, France); Ilpo Laine(Joensuu, Finland); Jacques Sauloy (Toulouse, France);Rod Halburd (Loughborough, UK); Decio Levi (Rome,Italy); Junkichi Satsuma (Tokyo, Japan); Peter E. Hydon(Surrey, UK); Jean-Marie Maillard (Paris, France);Walter van Assche (Louvain, Belgium); GertruidaImmink (Groningen, Netherlands); Frank Nijhoff(Leeds, UK); Alexander Veselov (Loughborough, UK);Arieh Iserles (Cambridge, UK); Vassilis Papageorgiou(Patras, Greece); Pawel Winternitz (Montreal, Canada)Programme: available on-line Chairs: Claude Viallet (CNRS Paris, France), JarmoHietarinta (University of Turku, Finland) Sponsors: European Commission, Research DG,Human Potential Programme, High-Level ScientificConferences (Contract No: HPCF-CT-2001-00013),INTASLocation: VVF Presquîle de Giens La Badine Grants: available in particular for nationals under 35from EU or associated states (Bulgaria, Cyprus, CzechRepublic, Estonia, Hungary, Iceland, Israel, Latvia,Liechtenstein, Lithuania, Norway, Poland, Romania,Slovakia and Slovenia). Some support will also beavailable for scientists of 35 years old or under from theNew Independent States of the former Soviet Union(NIS) Deadline: for grants, 28 MarchInformation: contact Rachid Adghoughi(radghoughi@esf.org), Conference Organiser, EuropeanScience Foundation, Euresco Office, 1 quai Lezay-Marnésia, 67080 Strasbourgweb site: http://www.esf.org/euresco/02/pc02185

24-27: International Workshop on Orthogonal

Polynomials: Orthogonal Polynomials andApproximation Theory (IWOP02), Leganes,Madrid, Spain Topics: approximation theory, quadrature formulas,orthogonal polynomialsMain speakers: J.S. Geronimo (Atlanta, USA), P.Gonzalez Vera (La Laguna, Spain), L. Jodar (Valencia,Spain), A.B.J. Kuijlaars (Leuven, Belgium), A.Martinez-Filkenshtein (Almeria, Spain), H. Stahl(Berlin, Germany)Abstracts: if you wish to present an oralcommunication, submit your abstract (plain ASCII orLaTeX, up to two pages) via the web siteScientific committee: Jesus Dehesa (Granada), AntonioDuran (Sevilla), Guillermo Lopez Lagomasino (Madrid),Paco Marcellan (Madrid), Walter Van Assche (Leuven)Organising committee: Renato Alvarez-Nodarse(Sevilla: ran@us.es), Jorge Arvesu (Madrid:jarvesu@math.uc3m.es) and Paco Marcellan (Madrid:pacomarc@ing.uc3m.es)Proceedings: a special volume of the proceedings isplannedLocation: Escuela Politecnica Superior, UniversidadCarlos III de Madrid, Leganes, Spain Deadline: for abstracts, 30 April Information: contact members of the organisingcommitteeweb site: http://merlin.us.es/~renato/iwop02/

24-28: Conference on Mathematical Modelling ofPopulation Dynamics, Bêdlewo, PolandInformation: web site:http://www.math.us.edu.pl/cmmpd/[For details, see EMS Newsletter 42]

25-28: International Conference dedicated to the65th Anniversary of B.N. Pshenichnyi (1937-2000),Kyiv, UkraineScope: optimisation, mathematical theory of control,dynamic games Topics: necessary conditions for extremum,mathematical programming, computational methods ofoptimisation, convex analysis and theory of set-valuedmappings, dynamic games, search for moving objects,mathematical theory of control, identification andminimax estimation of parameters, models of economicdynamics, decision making under uncertainty,optimisation problems of the charged particle beamdynamics, controlled processes simulation, applicationsin all areas Main speakers: A. Azimov (Turkey), A.B. Kurzhanski(Russia), Y.S. Ledyaev (Russia), A.G. Chentsov(Russia), A.A. Chikrii (Ukraine), V.S. Melnik (Ukraine),V.F. Demyanov (Russia), B. Mordukhovich (USA), A.Ioffe (Israel), A. Rubinov (Australia), F.M. Kirilova(Belarus), V.M. Tikhomirov (Russia)Call for papers: authors are invited to submit anelectronic version of their extended abstract (one fullsingle-spaced A4 page in English, LaTeX format): thename, affiliation and e-mail of the author are to beshown under the title of the paper. Address forsubmission of abstracts: shiran@mmsa.ntu-kpi.kiev.ua.The files should also be sent to the conference chair:chik@d165.icyb.kiev.ua Programme: lectures and contributed papersProgramme committee: Chair: I.V. Serhienko(Ukraine); Co-Chairs: M.Z. Zhurovskii and V.M.Kuntsevich (Ukraine); Members: A. Azimov (Turkey),V.D. Batukhtin (Russia), L. Berkovitz (USA), A.G.Chentsov (Russia), F.L. Chernousko (Russia), A.A.Chikrii (Ukraine), F. Clarke (Canada), J.-P. Dedieu(France), V.F. Demyanov (Russia), G. Feichtinger(Austria), R.F. Gabasov (Belarus), E. Galperin (Canada),F. Giannessi (Italy), O. Hajek (USA), J.-B. Hiriart-Urruty (France), Y.C. Ho (USA), F. Imado (Japan), A.Ioffe (Israel), J. Kaluski (Poland), F.M. Kirilova(Belarus), I.N. Kovalenko (Ukraine), N.N. Krasovskii(Russia), J. Krawczyk (New Zealand), A.V.Kryazhymskii (Russia), A.B. Kurzhanski (Russia), Y.S.Ledyaev (Russia), V.N. Malozyomov (Russia), V.Marchenko (Belarus), A.A. Melikyan (Russia), V.S.Melnik (Ukraine), A. Meystel (USA), Ye.F. Mishchenko(Russia), B. Mordukhovich (USA), M.S. Nikolskii(Russia), Yu.S. Osipov (Russia), M. Papageorgiou(Greece), P. Pardalos (USA), Z. Parsa (USA), J.-P.Penot (France), V.N. Redko (Ukraine), A. Rubinov

(Australia), N.Z. Shor (Ukraine), I.V. Skrypnyk(Ukraine), M. Thera (France), V.M. Tikhomirov(Russia), V.Ye. Tretyakov (Russia), V.O. Zhukovskii(Russia) Organising committee: A.A. Chikrii (Chair, Ukraine)Organisers: Glushkov Institute of Cybernetics of theNational Academy of Sciences, Institute for AppliedSystem Analysis of the National Academy of Sciencesand the Ministry of Education and Science of Ukraine,National Technical University Kyiv PolytechnicalInstitute Book of abstracts: to be published Location: in Kyiv, on the campus of the NationalTechnical University KPI Deadline: for submission of abstracts, 15 AprilInformation: web site:www.icyb.kiev.ua/conferences/conferences.html

25-28: 8th International Conference on Applicationsof Computer Algebra, Volos, GreeceThemes: computer algebra, symbolic computation Topics: computational quantifier elimination, computeralgebra and cagd, numerical-symbolic methods inphysical modelling, Gröbner bases and applications,robotics, mathematical physics and control theory, non-standard applications, industrial and engineeringapplications of computer algebra, symbolic and exactlinear algebra, automatic theorem proving, celestialmechanics, combinatorial and computational methods inalgebraic geometry and singularities, mathematicalimplementations, algebraic tools for differentialequations, computer algebra in education, dynamicalsystems and mechanics, new developments inmathematica, approximate algebraic computation andstabilisation, symbolic-numerical methods incomputational science, computational commutative anddifferential algebra General chairs: Alkiviadis G. Akritas, Ilias S. Kotsireas Administrative assistance: Theodora Terlexi Programme chairs: Victor Edneral, Eugenio Roanes-Lozano Organising committee: Stanley Steinberg, MichaelWesterLocal arrangements committee: Thomas Kylindris,Yiannis Parassidis, Korina D. Tsilika, Loukas ZachilasScientific committee: ACA Working Group, A.G.Akritas, (Greece), J. Calmet (Germany), V. Edneral(Russia), V. Ganzha (Germany), V. Gerdt (Russia), H.Hong (USA), E. Kaltofen (USA), I.S. Kotsireas(Canada), B. Kutzler (Austria), R. Liska (CzechRepublic), B. Pletsch (USA), E. Roanes-Lozano (Spain),S. Steinberg (USA), Q. Tran (USA), N. Vassiliev(Russia), M. Wester (USA)Sponsors: Greek Ministry of Culture, WaterlooMAPLE, Greek Telecommunications Organisation,Wilfrid Laurier University, University of Thessaly,Greek Railways, Ontario Research Centre For ComputerAlgebra, Alpha Bank, Texas Instruments, Wiley,IMACS, Cotopaxi, City of Volos Proceedings: a volume with the abstracts of the paperspresented at ACA 2002 will be available at theconference. Participants should submit their abstracts intext or LaTeX form to the session organisers. Selectedfull papers from those presented at the conference, aswell as at ACA 2001, will be published in a special issueof the Journal of Symbolic Computation, entitledSpecial Issue on Applications of Computer AlgebraDeadlines: for submissions of abstracts, 20 April; forsubmissions of full papers, 30 December Location: University of Thessaly, Department ofComputer Engineering, Telecommunications andNetworks Information: phone: + 30-421-074886, e-mail:aca2002@uth.gr web site: http://www.orcca.on.ca/~ilias/aca2002.html

27- 3 July: Fifth International Conference on Curvesand Surfaces, Saint-Malo, FranceInformation: web site: http://www-lmc.imag.fr/saint-malo/[For details, see EMS Newsletter 42]

27-2 July: 19th International Conference onOperator Theory, Timisoara, RomaniaTopics: operator theory, operator algebras and theirapplications: differential operators, complex functions,

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mathematical physics, matrix analysis, systems theory,etc. Main speakers (tentative): A. Atzmon (Israel), J.Bellissard (France), L.G. Brown (USA), I. Gohberg(Israel), Ch.R. Johnson (USA), L. Kerchy (Hungary), R.Nest (Denmark), J.R. Partington (England), R. Rochberg(USA), M. Rordam (Denmark), Z.J. Ruan (USA), G.Weiss (USA)Programme committee: W.B. Arveson (USA), N.K.Nikolskii (France), N. Salinas (USA), S. Stratila(Romania), F.H. Vasilescu (France)Proceedings: expected to be published Location: West University of Timisoara Sponsors: Institute of Mathematics of the RomanianAcademy and West University of Timisoara Grants: some financial support for PhD students andyoung researchers will be available: contact also theEURROMMAT programme(http://pompeiu.imar.ro/~eurrommat/positions.html)Deadlines: for registration, 30 MarchInformation: e-mail: ot@imar.ro web site: http://www.imar.ro/~ot

30-14 July: Lets Face Chaos through NonlinearDynamics, 5th International Summer School andConference, Maribor, Slovenia[dedicated to the 75th birthday of Prof. Hermann Haken] Themes: non-linear dynamics, chaos theory,synergetics, complex systems Scope: lecture courses (delivered by invited speakers)starting at introductory level adapted to seniorundergraduate and graduate students, and concludingwith the most recent research results comprehensible formost of the audience and subject to discussion amongthe attending invited speakers, experts and specialistsAim: scientific exchange among seemingly distantdisciplines, allowing students and junior scientists tounderstand better the role of interdisciplinary research, tobring them in touch with science in making, and to offerthe opportunity to present their own research work (inshort reports and posters)Topics: atomic physics, biophysics, chaos, classicalmechanics, computational physics, condensed matter,electromagnetism, fluid dynamics, general physics,mathematical physics, mathematics, medical physics,mesoscopic physics, molecular physics, non-lineardynamics, plasma physics, quantum chaos, quantummechanics, solid state physics, statistical physics,theoretical physics Invited lecturers: Y. Aizawa (Japan), V. Anishchenko(Russia), O. Bohigas (France), T. Bountis (Greece), G.Casati (Italy), P. Cvitanovic (USA), T. Frank(Netherlands), H. Fujisaka (Japan), G. Gallavotti (Italy),P. Gaspard (Belgium), I. Grabec (Slovenia), S.Grossmann (Germany), I. Guarneri (Italy), F. Haake(Germany), H. Haken (Germany), H. Hasegawa (Japan),Y. Kuramoto (Japan), J. Laskar (France), M. Matsushita(Japan), P. McClintock (UK), E. Mosekilde (Denmark),K. Nakamura (Japan), D. Pagon (Slovenia), J. Pichard(France), P. Prelovsek (Slovenia), T. Prosen (Slovenia),M. Robnik (Slovenia), V. Romanovski (Slovenia), M.Rosenblum (Germany), A. Ruffing (Germany), J.Schumacher (Germany), T. Seligman (Mexico), A.Shudo (Japan), M. Sonis (Israel), A. Stefanovska(Slovenia), H. Stoeckmann (Germany), G. Tanner (UK),P. Tass (Germany), J. Weele (Netherlands), M.Wilkinson (UK) Programme: 77 invited 60-minute lectures, at schooland conference level; opportunities to present researchwork as a short report (20 minutes) or poster; a richcultural and social programmeCall for papers: apply with abstract (posters or shortreport); see http://www.camtp.uni-mb.si/chaos/2002/apply.html Organising committee: director: M. Robnik (CAMTP,Slovenia); honorary directors: G. Casati (Italy), P.Cvitanovic (USA), S. Grossmann (Germany), H. Haken(Germany); members: Y. Aizawa (Japan), T. Bountis(Greece), H. Hasegawa (Japan), I. Mozetic (Slovenia), J.Pichard (France), T. Prosen (Slovenia), A. Ruffing(Germany), A. Stefanovska (Slovenia) Sponsors: Ministry of Education, Science and Sport,Nova Kreditna Banka Maribor, Telekom Slovenia Proceedings: accepted papers will be published,together with the lectures of invited speakers, as aspecial volume of the Supplement of Progress in

Theoretical Physics (Kyoto, Japan)Location: CAMTP: Center for Applied Mathematicsand Theoretical Physics, University of Maribor Krekova2, Maribor, SloveniaGrants: limited financial support for participants fromEastern European and developing countries. Apply by e-mail to chaos-support@uni-mb.si Deadlines: for application with abstract (poster orreport) or without presentation, 15 May; for lateapplication, 27 June; for application for financialsupport, 18 April; for hotel reservation , 27 June Information: e-mail: chaos@uni-mb.si http://www.camtp.uni-mb.si/chaos/2002/

1-5: Congrès de mathématiques appliquées à lamémoire de Jacques-Louis Lions, Paris, France Speakers: L. Ambrosio, F. Baccelli, J. Ball, F. Brezzi,L. Caffarelli, M.-P. Cani, A. Chorin, J.-M. Coron, L.Evans, O. Faugeras, M. Fink, M. Ghil, T. Hou, A.Majda, L. Nirenberg, G. Papanicolaou, A. Patera, B.Perthame, R. Rannacher, P. Souganidis, E. Tadmor, S.Varadhan, C. Villani, M. Vishik, J.-C. Yoccoz, E.Zuazua Honour committee: H. Curien, H. Fujita, P. Lax, E.Magenes (Chair), G. Marchuk Patronages: International Mathematical Union andAcadémie des Sciences de Paris Supported andsponsored by: Ministère de la Recherche, CNRS, CNES,INRIA, Collège de France, Ecole Polytechnique,Université Pierre et Marie Curie (Paris VI), SMAI andSMF Location: Collège de FranceRegistration: free of charge: please register directly onthe web siteInformation: postal address: Laboratoire danalysenumérique Université Pierre et Marie Curie Boî tecourrier 187 75252 Paris cedex 05 France, fax : + 33 1 44 27 72 00, e-mail: congres.jllions@ann.jussieu.fr web-site: http://acm.emath.fr/congres-jllions/

1-6: Advanced Course on Mathematical Finance:Models, Bellaterra, Barcelona, SpainCoordinator: Joan del CastilloInformation: web site: http://www.crm.es/matfin

1-6: 2nd International Conference on the Teachingof Mathematics at Undergraduate Level,Chersonissos, Crete, GreeceInformation: web site: http://www.math.uoc.gr/~ictm2[For details, see EMS Newsletter 42]

1-6, 2002 Workshop on Wavelets and Applications,Barcelona, SpainTopics: EDPs, numerical analysis, probability theory,signal processing Main speakers: C. Canuto (Politecnico di Torino), R.Gundy (Rutgers U.), T. Nguyen (U. California, SanDiego), A. Tabacco (Politecnico di Torino), G. Weiss(Washington U.) Intended audience: graduate students and youngresearchers Organising committee: M.J. Carro, J. Cerda, J. Martin,J. Soria Sponsors: Institute of Mathematics of the University ofBarcelona (IMUB) Location: University of Barcelona, Gran Via 585,08007 Barcelona Deadlines: for registration, 31 MayInformation: http://www.imub.ub.es/wavelets

2-6: 2002 Barcelona Conference on AlgebraicTopology (a EuroConference), Barcelona, SpainInformation: web site: http://www.crm.es/2002bcat

2-6: 5th Conference of the European Society ofMathematics and Theoretical Biology onMathematical Modelling and Computing in Biologyand Medicine, Milano, Italy Aim: to foster interdisciplinary collaboration betweenmathematicians and bioscientists and to act as the mainforum for the exchange of recent research results andnew research directions to the widest possible

July 2002

community in theoretical biology and medicine inEurope and beyondTopics: biotechnology and bioengineering,bioinformatics and computational biology, biomedicalimaging, cardiovascular system, cell signalling, cellularorganisation, ecology, environmental sciences,evolution, immunology, infectious diseases, individualbased models, computational neuroscience, visualisation,regulatory gene networks Main speakers: Marina Alexandersson (Sweden),Giuseppe Baselli (Italy), Tom Britton (Sweden), KlausDietz (Germany), Wulfram Gerstner (Switzerland),Hans-Christian Hege (Germany), Claudia Neuhauser(USA), A. Neumann (Israel), Alfio Quarteroni (Italy),Jonathan Sherratt (UK), Karl Sigmund (Austria), DenisThieffry (France), Daniel Tranchina (USA), TamikiUmeda (Japan), Hans Westerhoff (Netherlands), SimonWood (UK)Programme: organised in sections, each comprising aninvited speaker and 2-hour mini-symposia; posters canbe presented in special sessions ESMTB Board: V. Capasso (President), Z. Agur, O.Arino, M. Chaplain, M. Gyllenberg, J.A.P. Heesterbeek,M. Kaufman, V. Krivan, A. Stevens, P. Tracqui Programme committee: P. Cinquin, A. De Roos, P.Deuflhard, A. Goldbeter, P. Jaegers, W. Jager, P.Lansky, P. Maini, H. Metz, R. Nisbet, C. Peskin, S.Rinaldi, L. Segel. Liaisons: A. Hastings (SMB), M.Mimura (JSMB) Organising committee: V. Capasso, E. Beretta, P.Cerrai, P. Colli-Franzone, S. Cerutti, A. De Gaetano, A.Fasano, P. Fergola, A. Gandolfi, E. Galli, M. Gatto, F.Grandoni, A. Mari, C. Matessi, A. Morabito, D. Morale,G. Naldi, S. Paveri-Fontana, L. Preziosi, A. Pugliese, L.Sacerdote Sponsors: European Union, Centro Nazionale delleRicerche Universita degli Studi di Milano, Politecnicodi Milano, Milan Research Centre for Industrial andApplied Mathematics (MIRIAM), Universita degliStudi di Pavia, MURST-COFIN Processi Stocastici aStruttura Spaziale, Domus Galilaeiana,STMicroelectronics Grants: more than 100 fellowships for eligible (lessthan 35 years and members of the Union or anAssociated State) young researchers have beensupported by the European Union. Probably somesupport will be available without the EU criteria Deadlines: for applications for financial support, passed;for early registration, 1 April; for papers, 31 DecemberInformation: e-mail: ecmtb@mat.unimi.it web site: http://ecmtb.mat.unimi.it

7-14: 6th WSEAS CSCC Multiconference onCircuits; Systems; Communications; Computers;Applied Informatics; Signal Processing andComputational Geometry and Vision; ScientificComputations and Soft Computing, RethymnaBeach, CreteInformation: e-mail: manolis7@wseas.orgweb site: http://www.wseas.org/conferences/2002/crete

8-26: School and Conference on Algebraic K-theoryand its Applications, Trieste, ItalyTheme: K-theory and related topics Aim: to update information on recent developments inthe field and re-emphasise the multidisciplinary nature ofK-theory and its usefulness in solving problems arisingin several areas of mathematicsTopics: K-theory and algebraic topology; K-theory andnon-commutative geometry; a survey of thedevelopments of K-theory in the last 45 years; K-theoryand arithmetics; K-theory and representation theory; K-theory and algebraic geometryMain speakers: L. Barbieri-Viale (Italy), J. Berrick(Singapore), S. Bloch (USA), J. Cuntz (Germany), E.Friedlander (USA), H. Gillet (USA), L. Hesselholt(USA), N. Higson (USA), R. Jardine (Canada), B. Kahn(France), M. Karoubi (France), M. Kolster (Canada),A.O. Kuku (Italy), M. Levine (USA), S. Lichtenbaum(USA), J.-L. Loday (France), W. Lueck (Germany), P.May (USA), F. Morel (France), I. Panin (Russia), E.Pedersen (USA), C. Pedrini (Italy), U. Rehmann(Germany), J. Rosenberg (USA), S. Saito (Japan), V.P.Snaith (UK), C. Soulé (France), V. Voevodsky (USA),C. Weibel (USA) Programme: the first two weeks (8-19 July) will

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comprise invited expository lectures on several aspectsof the field; the last week (22-26 July) will be aConference featuring mainly research lectures by invitedspecialists, with possible contributions by some selectedparticipants Organising committee: M. Karoubi (France), A.O.Kuku (Italy), C. Pedrini (Italy)Sponsor: Abdus Salam International Centre forTheoretical PhysicsProceedings: will be published Location: Abdus Salam International Centre forTheoretical Physics (Strada Costiera 11, Trieste) Grants: some financial grants are available forapplicants from, and working in, developing countriesonly, to be selected by the organisers; there may also beother support for participants from European countriesDeadline: already passed Information: e-mail: smr1418@ictp.trieste.it web site: http://www.ictp.trieste.it/www_users/math/maths2002.html

10-13 VISIT-ME-2002 (Vienna InternationalSymposium on Integrating Technology intoMathematics Education), Vienna, Austria Aim: to bring together experts and non-experts with aninterest in this topicTopics: include CAS-based curricula and teachingmethods, dynamic geometry systems as teaching tools,assessing with technology, internet as a teaching aid,dispensable and indispensable mathematical skills andabilities, CAS as pedagogical tools for visualisation,experimentation, concentration, new classroomexamples using CAS, the next generation: PeCAS =Pedagogical CAS, applications in mathematics, thenatural sciences, research and development, economy,social sciences, industry, interfaces to otherprograms/tools, producing and using utility files,programming in Derive, TI-89/92, and other CAS,problems and limitations, web resources going on-line,teaching and learning with Derive and other CAS,connecting computer algebra and computational logic Main speakers: Bruno Buchberger (Austria), Miguel deGuzman (Spain), Albert Rich (USA), Hans-GeorgWeigand (Germany) Languages: English and German Programme committee: Josef Boehm (Austria), VlastaKokol-Voljc (Slovenia), Bernhard Kutzler (Austria),Carl Leinbach (USA), Brian Denton (UK), WilfriedHerget (Germany), Jean-Baptiste Lagrange (France),Edith Schneider (Austria), James Schultz (USA),Marlene Torres-Skoumal (Austria), BernardWinkelmann (Germany), Michel Beaudin (Canada),Josef Lechner (Austria), Francisco Puerta (Spain),Eugenio Roanes (Spain), Theresa Shelby (USA), DavidSjoestrand (Sweden), Hubert Weller (Germany), JohannWiesenbauer (Austria) Organising committee: Josef Boehm (Austria), HelmutHeugl (Austria), Bernhard Kutzler (Austria) Sponsors: Austrian Ministry of Education, SoftWarehouse Europe, Texas Instruments Proceedings: to be published with an ISBN on CD-ROM Location: University of Vienna, Strudlhofgasse, Vienna,Austria e-mail: b.kutzler@eunet.atweb site: http://www.acdca.ac.at/visit-me-2002

15-18: Modular Curves and Abelian Varieties(EuroConference), Bellaterra, Barcelona, SpainCoordinator: J. QuerInformation: web site: http://www.crm.es/mcav02

16-22: 7th International Spring School: NonlinearAnalysis, Function Spaces and Applications (NAFSA7), Prague, Czech RepublicInformation: web site: http://www.math.cas.cz/~nafsa7[For details, see EMS Newsletter 40]

22-25: IEEE Symposium on Logic in ComputerScience (LICS02), Copenhagen, Denmark [part of the 2002 Federated Logic Conferences FloC02]Topics: automata theory, automated deduction,categorical models and logics, concurrency anddistributed computation, constraint programming,constructive mathematics, database theory, domain

theory, finite model theory, formal aspects of programanalysis, formal methods, hybrid systems, lambda andcombinatory calculi, linear logic, logical aspects ofcomputational complexity, logics in artificialintelligence, logics of programs, logic programming,modal and temporal logics, model checking,programming language semantics, reasoning aboutsecurity, rewriting, specifications, type systems and typetheory, and verificationMain speakers: Stephen Cook (University of Toronto),Georg Gottlob (TU Wien), John Reynolds (CarnegieMellon), Natarajan Shankar (SRI), Maurizio Lenzerini(Universita di Roma La Sapienza) Programme committee: Franz Baader (Aachen),Marco Cadoli (Rome), Vincent Danos (Paris), AnujDawar (Cambridge), Rocco De Nicola (Firenze), HaraldGanzinger (Saarbrücken), Orna Grumberg (Haifa),Robert Harper (Carnegie Mellon), Furio Honsell(Udine), Phokion Kolaitis (Santa Cruz), JohannMakowsky (Haifa), Oded Maler (Grenoble), YoramMoses (Haifa), Robert Nieuwenhuis (Barcelona), PeterOHearn (London), Doron Peled (Austin), BenjaminPierce (Philadelphia), Andrew Pitts (Cambridge),Gordon Plotkin (Chair, Edinburgh), Andreas Podelski(Saarbrücken), Andre Scedrov (Philadelphia), PeterThiemann (Freiburg), Andrei Voronkov (Manchester) Information: e-mail: lics-request@dcs.ed.ac.ukweb site:http://www.dcs.ed.ac.uk/home/grohe/lics/lics02/

22-26: Universal Algebra and Lattice Theory,Szeged, Hungary[dedicated to the 70th birthday of B. Csakany] Main speakers: J. Berman (Chicago), P. Dehornoy(Caen), M. Goldstern (Vienna), E.W. Kiss (Budapest),M. Maroti (Nashville), P.P. Palfy (Budapest), I.G.Rosenberg (Montreal)Call for papers: we are using the facilities of AtlasMathematical Conference; if you wish to present a talk,please submit your abstract at http://at.yorku.ca/cgi-bin/amca/submit/caiv-01 Programme committee: J. Jezek (Prague), K. Kearnes(Boulder), R. Poeschel (Dresden), A. Romanowska(Warsaw), A. Szendrei (Szeged), R. Willard (Waterloo)Organising committee: A. Szendrei (Szeged), L. Szabo(Szeged), M. Dorman (Szeged) Grants: reduction of the registration fee or contributionto accommodation costs may be provided upon requestfor some participants, especially for students and youngpeople who are not supported by their universitiesDeadlines: for registration, 15 April; for abstracts: 1JulyInformation: e-mail: algebra@server.math.u-szeged.hu web site: http://www.math.u-szeged.hu/confer/algebra/2002/

3-9: Logic Colloquium 2002 (ASL EuropeanSummer Meeting), Muenster, Germany[change of date]Sponsors: Association of Symbolic Logic, WestfälischeWilhelms-Universität Münster Rheinische Friedrich-Wilhelms-Universität Bonn DeutscheForschungsgemeinschaft Deadlines: for travel grants, 1 April; for submission ofabstracts, 1 MayNote: satellite meeting: Colloquium Logicum 2002 Information: web site: http://www.math.uni-muenster.de/LC2002/[For details, see EMS Newsletter 41]

5-9: International Conference on Ill-Posed andInverse Problems, Novosibirsk, RussiaInformation: web site:www.math.nsc.ru/conference/mml[For details, see EMS Newsletter 42]

9-11: Colloquium Logicum 2002, 2nd BiannualMeeting of the DVMLG, Münster, Germany[satellite meeting of Logic Colloquium 2002]Organising and scientific committee: Justus Diller(Münster), Peter Koepke (Bonn), Benedikt Löwe(Bonn), Wolfram Pohlers (Münster, Chair), ChristianThiel (Erlangen), Wolfgang Thomas (Aachen), Andreas

August 2002

Weiermann (Münster) Invited speakers: Toshiyasu Arai (Hiroshima), JoanBagaria (Barcelona), André Nies (Chicago), Martin Otto(Swansea), Charles Parsons (Cambridge, USA), AnandPillay (Urbana-Champaign), Michael Rathjen (Leeds),Johan van Benthem (Amsterdam- Stanford)Sponsors: Deutsche Vereinigung für MathematischeLogik und für Grundlagen der Exakten Wissenschaften(DVMLG) Deutsche Forschungsgemeinschaft Information: web site: http://wwwmath.uni-muenster.de/LC2002/CL2002.html

10-11: Colloquium Logicum 2002, Münster,Germany[satellite conference of Logic Colloquium 2002]Information: web site: http://wwwmath.uni-muenster.de/LC2002/[For details, see EMS Newsletter 41]

25-30: Wireless and Optical Communications(WOC02), Miedzyzdroje, PolandInformation: web site:http://www.worldses.org/wses/calendar.htm

25-30: Nanoelectronics, Nanotechnologies (NN02),Miedzyzdroje, PolandInformation: web site:http://www.worldses.org/wses/calendar.htm

27-2 September: Third International School-symposium: Symmetry and CosymmetryApplications in the Theory of Bifurcations and PhaseTransitions, Big Sochi, RussiaTheme: mathematical physicsTopics: symmetry and cosymmetry, theory ofbifurcations, phase transitionsProgramme: symmetry in classical mechanics,integrability of conservative systems, connection withsymmetry and cosymmetry, conservative chaos,convection of homogeneous and multicomponent fluids phase transitions, bifurcation, asymptotic models,influence of electromagnetic field, convection of fluid ina porous medium, chaotic motions, phase transitions inferro- and antiferro-magnets and in liquid crystals,symmetry and cosymmetry influence, symmetry andcosymmetry in classical hydrodynamics, theory ofstationary motions and their stability, applications tohydrodynamics and others fields of mathematicalphysics, magnetodynamics problemsSessions: Section 1: Phase transitions in continuousmedia and scenarios of chaos origin; Chairs VictorYudovich (Russia), George Zaslavsky (USA). Section2: Phase transitions in solid states and fluids; ChairsJakow Granovskii (Poland), Yurii Gufan (Russia)Programme committee and main speakers: V.Yudovich (Russia), V. Pukhnachev (Russia), Yu. Gufan(Russia), E. Vinberg (Russia), G. Zaslavsky (USA), G.Iooss (France), G-F. Sartory (Italy), J. Granovskii(Poland), B. Karasözen (Turkey), Jai Sam Kim (SouthKorea), A. Sadkov (Russia) Organising committee: V. Yudovich (Russia), Yu.Gufan (Russia), J. Erusalimsky (Russia), A. Sadkov(Russia)Languages: English and Russian Call for papers: 2-page extended abstracts must besubmitted by e-mail to sadkov@ip.rsu.ru oryudovich@math.rsu.ruSponsors (provisional): RFBR and INTASProceedings: to be publishedLocation: camping Slava on the Big Sochi coast of theBlack Sea Grants: we may be able partially to reimbursesubsistence expenses for young scientists, students andlecturersDeadlines: for registration, 1 June; for abstracts, 1 JulyInformation: e-mail: sadkov@ip.rsu.ru oryudovich@math.rsu.ruweb site:http://www.math.rsu.ru/mexmat/kvm/school2002

1-9: 8th AHA 2002, International Congress onAlgebraic Hyperstructures and Applications,Samothraki Island, Greece

September 2002

CONFERENCES

EMS March 200234

Topics: hypergroups, semi-hypergroups,hypergroupoids, hyperrings, hyperfields, hypervectorialspaces, Hv-structures (Hv-groups, semigroups, rings),non-associative and feebly associative hypergroupoids,join spaces, hyperstructures associated with geometricspaces, ordered hyperstructures, fuzzy hyperstructures,hypergraphs, generalisations and applicationsMain speakers: P. Corsini (Italy), Y. Sureau (France), I.Rosenberg (Canada), S. Comer (USA), J. Jantosciak(USA), J. Mittas (Greece), R. Migliorato (Italy), V.Loereanu (Romania), M.M. Zahedi (Iran), M.Konstantinidou-Serafimidou (Greece)Call for papers: to present an oral communication,submit an abstract (type and centre the title, in capitals,authors name and affiliation in this order; restrict yourtext to 200 words) via aha2002@agro.duth.grProgramme committee: P. Corsini (Italy), S. Comer(USA), J. Jantosciak (USA), M. Konstantinidou-Serafimidou (Greece), R. Migliorato (Italy), I.Rosenberg (Canada), S. Spartalis (Greece), Y. Sureau(France), T. Vougiouklis (Greece)Organising committee: T. Vougiouklis (Greece), S.Spartalis (Greece), H. Sakonidis (Greece) Sponsors: Democritus University of Thrace, HellenicMinistry of EducationProceedings: to be published Location: Hotel Aeolos, Samothraki Island, GreeceDeadlines: for registration, 31 March; for abstracts, 30April; for hotel deposit 30 June Information: e-mail: aha2002@agro.duth.gr,tvougiou@edu.duth.gr, sspart@utopia.duth.gr

3-7: 8th International Conference on Stability,Control and Rigid Bodies Dynamics, Donetsk,UkraineInformation: web site:http://www.iamm.ac.donetsk.ua/conf2002.html[For details, see EMS Newsletter 42]

4-6: Fourth International Workshop on AutomatedDeduction in Geometry, RISC-Linz,Hagenberg/Linz, Austria Theme: automated deduction in geometry Topics: polynomial algebra, invariant and coordinate-free methods, probabilistic, synthetic, and logicapproaches, techniques for automated geometricreasoning from discrete mathematics, combinatorics, andnumerics, symbolic and numeric methods for geometriccomputation, geometric constraint solving, automatedgeneration/reasoning and manipulation with diagrams,design and implementation of geometry software,special-purpose tools, automated theorem provers,experimental studies, applications of ADG to mechanics,geometric modelling, CAGD/CAD, computer vision,robotics and educationMain speakers: two invited talks: names of speakers tobe announced shortlyCall for papers: see the web siteProgramme committee: Shang-Ching Chou (Wichita,USA), Andreas Dress (Bielefeld, Germany), DesmondFearnley-Sander (Hobart, Australia), Xiao-Shan Gao(Beijing, China), Hoon Hong (Raleigh, USA), DeepakKapur (Albuquerque, USA), Josef Schicho (Linz,Austria), Bernd Sturmfels (Berkeley, USA), Gert Vegter(Groningen, Netherlands), Dongming Wang (Paris,France), Volker Weispfenning (Passau, Germany), NeilWhite (Gainesville, USA), Franz Winkler (Linz,Austria), Chair Lu Yang (Chengdu, China) Organising committee: F. Winkler (Chair, Austria), M.Athale (Austria) Proceedings: authors of extended abstracts and fullpapers accepted for presentation will be invited tosubmit full and/or revised papers for publication in theproceedings of ADG 2002 after the workshop; thesubmitted papers will be formally reviewed by PCmembers and external referees. It is expected that theaccepted papers will be published as a volume in theLNAI series by Springer-Verlag. (The proceedings ofADG 96, ADG 98 and ADG 00 appeared as LNAI1360, LNAI 1669 and LNAI 2061)Location: Schloss Hagenberg (15km north of Linz), thehome of Johannes Kepler Universitys Research Institutefor Symbolic Computation (RISC-Linz): see the RISChomepage (http://www.risc.uni-linz.ac.at) for moreinformation Deadlines: extended abstract submission by 3 June,

notification of acceptance or rejection by 3 July, fullpaper submission by 4 NovemberInformation: e-mail: Franz.Winkler,Manasi.Athale@risc.uni-linz.ac.at web site: http://www.risc.uni-linz.ac.at/conferences/adg2002

4-6: 3rd International Conference on Mathematicaland Computational Applications, Konya, Turkey Theme: engineering, natural sciences or social scienceswhere mathematical and/or computational techniques arenecessary for solving specific problemsAim: to provide a medium by which a wide range ofexperiences can be exchanged among researchers fromdiverse fields such as engineering (electrical,mechanical, civil, industrial, aeronautical, nuclear etc.),natural sciences (physics, mathematics, chemistry,biology etc.) or social sciences (administrative sciences,economics, political sciences etc.)Scope: papers may be theoretical where mathematics isused in a non-trivial way or computational, or acombination of both; papers containing onlyexperimental techniques and abstract mathematicswithout any sign of application are discouragedTopics: papers will be submitted in two categories: (1)journal papers (only papers of the highest quality thatcontain original ideas and research will be published inthe journal Mathematical and ComputationalApplications); (2) conference papersCall for papers: we are using the facilities of Internetand International Journal of Applied Mechanics andEngineering (V. 6, No. 4, 2001)Programme committee: H. Adeli (USA), M. Akbaba(Bahrain), R. Aliev (Azerbaijan), N. Allahverdi(Turkey), S. Ay (Turkey), O. Balci (USA), A.Baykasoglu (Turkey), M. Bikdash (USA), N. Bildik(Turkey), F. Botsali (Turkey), D. Bozkurt (Turkey), B.Can (Turkey), M. Can (Turkey), Z. Celep (Turkey), A.Caliskan (Turkey), K. Carman (Turkey), T. Dereli(Turkey), A.H. Elkholy (Kuwait), K. Erciyes (USA), A.Erisen (Turkey), E. Murat Esin (Turkey), Z. Fazekas(UK), I. Guler (Turkey), K. Gulez (Japan), F. Gurgen(Turkey), E. Hasanov (Turkey), H. Huseynov (Turkey),C. Isci (Turkey), S. Kahramanli (Turkey), H. Kaplan(Turkey), H. Karagulle (Turkey), R. Karakuzu (Turkey),B. Karlik (Bahrain), M. Keskin (Turkey), S. Kocak(Turkey), A. Kuliev (Turkey), A. Kucukbursa (Turkey),A.C.J. Luo (USA), F.M. Mahomed (South Africa), D.L.Mitov (Bulgaria), P.M. Oliveira (Portugal), M.Pakdemirli (Turkey), J. Saleh (Jordan), E. Savas(Turkey), O. Sayman (Turkey), S. Selvi (Turkey), Z. Sen(Turkey), A. Sinan (Turkey), K. Soltanov (Azerbaijan),M. Tekelioglu (Turkey), O. Tokhi (UK), M. Turhan(Turkey), I. Uluer (Turkey), U. Uzman (Turkey), F.Unsacar (Turkey), G. Unal (Turkey), V. Vagin (Russia),A. Vidybida (Ukraine), E. Walicki (Poland), A. Yavas(USA), A.S. Yigit (Kuwait), Organising committee: N. Allahverdi (Turkey), K.Carman (Turkey), T. Sisman (Turkey), A. Gunes(Turkey), M.N. Ornek (Turkey), I. Saritas (Turkey), L.Civcik (Turkey) Location: Suleyman Demirel Culturel Centre, Campus,KonyaGrants: probably support for participants from countriesin a difficult economic situation and youngmathematiciansOrganisers: Technical Education Faculty of SelcukUniversity, Association for Scientific ResearchDeadlines: for full papers, passed; for registration, 30JuneInformation: e-mail: icmca2002@selcuk.edu.trweb site: http://www.selcuk.edu.tr/icmca2002

4-7: International Conference on Dynamical Methodsfor Differential Equations, Valladolid, SpainInformation: web site:http://wmatem.eis.uva.es/~dmde02/[For details, see EMS Newsletter 41]

4-7: Perspectives in Mathematical Physics, Rome,Italy[in honour of the 60th birthday of Prof. GiovanniGallavotti]Topics: mathematical physics, such as classical andquantum statistical mechanics, dynamical systems,hamiltonian perturbation theory, macroscopic limits,

fluid dynamicsSpeakers: include D. Brydges (Canada), L. Chierchia(Italy), E.G.D. Cohen (USA), G. DellAntonio (Italy), S.Doplicher (Italy), H. Epstein (France), J. Froelich(Swiss), L. Galgani (Italy), G. Gentile (Italy), S. Graffi(Italy), F. Guerra (Italy), G. Jona Lasinio (Italy), J.Lebowitz (USA), E. Lieb (USA), C. Liverani (Italy), R.Livi (Italy), C. Marchioro (Italy), S. Miracle-Sole(France), E. Olivieri (Italy), V. Rivasseau (France), D.Ruelle (France), Ya. Sinai (USA)Organising committee: G. Benettin (Italy), G. Benfatto(Italy), F. Bonetto (USA), M. Cassandro (Italy), A.Celletti (Italy), R. Esposito (Italy), C. Falcolini (Italy),A. Giorgilli (Italy), V. Mastropietro (Italy) Location: Department of Physics, University of RomaLa SapienzaNotes: there is no registration fee: only invitedcommunications will be presentedDeadline: for registration, 15 MayInformation:web site: http://www.mat.uniroma2.it/pmp2002

8-13: ALGORITMY 2002, Conference on ScientificComputing, High Tatra Mountains, Podbanske,SlovakiaInformation: web site: http://www.math.sk/alg2002[For details, see EMS Newsletter 42]

9-12 : Conference on Harmonic Analysis,Luxembourg-Metz (Luxembourg-France) Topics: non-commutative harmonic analysis,representation theory, real and complex analysis relatedto groups Organisers: Bachir Bekka, Jean Ludwig, CarineMolitor-Braun, Norbert Poncin; organised jointly by theCentre Universitaire of Luxembourg and the Universityof MetzLocation: Centre Universitaire of Luxembourg (9-10September) and University of Metz (11-12 September) Main speakers (preliminary list): C. Anantharaman-Delaroche, J.P. Anker, Y. Benoist, E. Damek, H.Fujiwara, H. Oh, E. Kaniuth, A. Lubotzky, D. Müller,K.H. Neeb, D. Poguntke, G. Robertson, W. Schmid, T.Steger, A. Valette, A.M. VershikProgramme: in addition to the regular conferenceprogramme, communication sessions for participants topresent their research in a 20-minute talk are plannedProceedings: speakers may publish their contribution ina special issue of the journal Travaux mathématiques,Publications du Centre Universitaire Grants: a limited number of grants will be available foryoung researchersSponsors: Fonds National de la Recherche(Luxembourg), Centre Universitaire de Luxembourg,Université de Metz, Laboratoire de Mathématiques(MMAS) de lUniversité de Metz Information: e-mail: harmonic_analysis@cu.lu web site: http://www.cu.lu/harmonic_analysis

10-20: Advanced Course on Geometric 3-Manifolds,Bellaterra, Barcelona, SpainCoordinator: Joan PortiInformation: web site: http://www.crm.es/geom-mani

20-25: International Conference on ComputationalMethods in Science and Eng. (CMMSE-2002),Alicante, SpainInformation: web site: www.ua.es/cmmse2002/[For details, see EMS Newsletter 42]

23-27: Ramification in Arithmetic and Geometry,Paris, FranceOrganisers: A. Abbes (Paris), B. Erez (Bordeaux), T.Saito (Tokyo)Location: Institut Galilee, Universite Paris 13Information: http://www-math.math.univ-paris13.fr/~ramifica/

25-28: 2nd WSEAS International Conferences on:Simulation, Modelling and Optimization; Signal,Speech and Image Processing; Multimedia, Internetand Video; Robotics, Distance Learning andIntelligent Communication Systems, Skiathos, GreeceInformation: e-mail: skiathos2002@wseas.orgweb site:http://www.wseas.org/conferences/2002/skiathos/

CONFERENCES

EMS March 2002 35

Books submitted for review should be sent to the fol-lowing address:Ivan Netuka, MÚUK, Sokolovská 83, 186 75 Praha8, Czech Republic.

J. Adams and D. Vogan (eds.), RepresentationTheory of Lie Groups, IAS/Park City MathematicalSeries 8, American Mathematical Society, Providence,2000, 340 pp., US$49, ISBN 0-8218-1941-0Each summer, there are a research programmeand a graduate summer school organised by theIAS/ParkCity Mathematics Institute. In 1998,the topic chosen was Representation theory ofreductive Lie groups. This book is a collection ofthe written versions of lectures presented there.

The lectures concentrate on the problem ofunderstanding irreducible representations ofreductive Lie groups. The lecture series by A.Knapp (delivered by P. Trapa) describes theLanglands parametrisation of irreducible(admissible) representations of such groups.The lectures by R. Zireau and L. Barchinidescribe cohomologically induced families ofunitary representations, which appear in har-monic analysis and the theory of authomorphicforms. The lectures by D. Vogan describe geo-metrical constructions of unitary representa-tions, using ideas of Kirillov and Kostant (themethod of coadjoint orbits). The lectures byK.Vilonen use geometrical tools (constructiblesheaves, semialgebraic sets and derived cate-gories) to recover the global character of repre-sentations constructed by infinitesimal methods.The last lecture in the book, by J.-S. Li,describes restrictions of a certain class of mini-mal representations to the so-called reductivedual pairs, introduced and studied by A. Weiland R. Howe.

Altogether, the volume brings a coherentdescription of an important and beautiful partof representation theory, which certainly will beof substantial use for postgraduate students andmathematicians interested in the area. (vs)

H. Amann and J. Escher, Analysis III,Grundstudium Mathematik, Birkhäuser, Basel,2001, 480 pp., ISBN 3-7643-6613-3 and 3-7643-6614-1This volume is devoted to integration and toglobal analysis. Integration theory is developedalong standard lines (measure spaces, measures,outer measure, integrability, Lebesgue measure,integrable functions, convergence theorem,Lebesgue spaces, Fubinis theorem, change ofvariables) with one notable exception: the inte-gration of Banach space-valued functions (theBochner-Lebesgue integral) is introduced sys-tematically. Much space is devoted to less tradi-tional subjects: convolutions, the Fourier trans-form on Schwartz spaces, distributions, lineardifferential operators, weak derivatives, Sobolevspaces, the Heisenberg uncertainty relation.The part on integration covers a half of the text,approximately 250 pages, and is accompaniedby 194 problems associated with the individualsections.

In the second part of the volume, about 160pages are devoted to manifolds in Euclideanspaces, multi-linear algebra, the theory of differ-ential forms, vector fields, the Riemann metricand vector analysis. The last part of the bookdeals with integration on manifolds: integrationof differential forms and Stokes theorem,including such special cases as the Gauss-Greentheorem, Greens formulae and the classical

Stokes theorem. In view of their applications,manifolds with a small singular part are allowed.The second part contains 100 problems for solu-tion.

The material included in this book exceedsthe volume usually covered in analysis courses,and may be used for seminars or for supple-mentary reading. The book is recommended tostudents and to teachers of mathematical analy-sis. (in)

Yu. Aminov, The Geometry of Vector Fields,Gordon and Breach Publishers, Amsterdam, 2000,172 pp., £45, ISBN 90-5699-201-5If we have a regular family of surfaces filling adomain in 3-dimensional Euclidean space in anice way (without mutual intersections), we canintroduce on this domain the field of unit nor-mals to the surfaces under consideration. Agreat deal of geometry of a regular family of sur-faces can be described in terms of this normalfield. Quite naturally, by the end of the nine-teenth century, the idea emerged of investigat-ing in a similar way a unit vector field that doesnot arise from a family of surfaces. In such a sit-uation one usually speaks about a non-holo-nomic vector field.

This monograph can be considered as anintroduction to the subject. We find here manyclassical results that are proved in a new andmodern way. It also contains plenty of recentresults, and consequently represents an intro-duction to contemporary research in the field. Itis divided into two chapters. The first chapterdeals with domains in 3-dimensional Euclideanspace and the vector fields on them, while thesecond passes to domains in higher-dimension-al Euclidean spaces, or even in Riemannianmanifolds. The authors also present interestingapplications, mostly in the dynamics of mechan-ical systems with non-holonomic constraints,and in the geometry of velocity fields of fluidflow. Quite recently, there have been applica-tions in the description of liquid crystals and fer-romagnets.

The prerequisites required for reading aremodest. Basic courses of analysis and classicaldifferential geometry should suffice. (jiva)

V. I. Arnold, M. F. Atiyah, P. Lax and B. Mazur(eds.), Mathematics: Frontiers and Perspectives,International Mathematical Union, AmericanMathematical Union, Providence, 2000, 459 pp.,US$49, ISBN 0-8218-2070-2The change of a millennium was an occasion toreflect on the state of mathematics and to try tosee future perspectives. This book collects thirtyarticles by leading mathematicians (half of themrecipients of the Fields Medal) on the occasionof the World Mathematical Year 2000.

Different articles are written with differentaims. Some of them bring a list of problems in achosen specific area, some are reviews of possi-ble future developments, others bring more per-sonal viewpoints. There are many articles show-ing how important has been the recent interac-tion between mathematics and theoreticalphysics for future development in mathematics.There are also articles on the connectionsbetween pure mathematics and certain areas ofapplied mathematics. The authors are M.F.Atiyah (preface), A. Baker, G. Wustholz, J.Bourgain, S.-S. Chern, A. Connes, S.K.Donaldson, W.T. Gowers, V.F.R. Jones, D.Kazhdan, F. Kirwain, P.-L. Lions, A.J. Majda,

Yu.I. Manin, G. Margulis, D. McDuff, S. Mori,D. Mumford, R. Penrose, K.F. Roth, D. Ruelle,P. Sarnak, S. Smale, R.P. Stanley, C. Vafa, A.Wiles, E. Witten, S.-T. Yau, V.I. Arnold, P.D. Laxand B. Mazur.

This book should be in the library of everyworking mathematician. (vs)

A. V. Balakrishnan (ed.), Semigroups ofOperators: Theory and Applications, Progress inNonlinear Differential Equations and TheirApplications 142, Birkhäuser, Basel, 2000, 367 pp.,DM 178, ISBN 3-7643-6310-XThis volume is the proceedings of the confer-ence on C0-semigroups and their applications,held at Newport Beach in December 1998.These proceedings consist of 35 contributions.Most of them are short (less than 10 pages), buta reader can nevertheless get a good insight intothe current research interests, both in theoryand applications. Most frequently, the attentionis paid to various aspects of stability and to ana-lytic semigroups (including generation theo-rems on Lie groups and fractional powers ofgenerators). Several papers are devoted to theinteraction between stochastic analysis and semi-group theory (Feller semigroups). Applicationsare given to problems in physics (fluid dynam-ics, aero-elasticity, Dirac equation and flutter ofwings) and control theory (thermo-elasticplates). (jmil)

S. Batterson, Stephen Smale: TheMathematician Who Broke the DimensionBarrier, American Mathematical Society,Providence, 2000, 306 pp., US$35, ISBN 0-8218-2045-1This is a biography of Stephen Smale, written bya mathematician who declares himself as his aca-demic grandson. To write this biographyinvolved tremendous work, but the result is bril-liant. It is designed to be accessible for non-mathematicians.

Smale is presented here first of all as a greatmathematician, and together with his personali-ty we gradually become familiar also with math-ematical life in the United States. The authordoes not avoid describing Smales mathematicalresults, but having in mind the aim of the book,he introduces them in a way that can be under-stood by most readers. For readers closer tomathematics, but still non-mathematicians, fourappendices are included, explaining his resultsin more detail. On the other hand, the authorsskilful presentation of Smales mathematical dis-coveries will surely attract the interest of profes-sional mathematicians. Every mathematicianknows Smales famous results (such as the high-er-dimensional Poincaré conjecture), but notmany of them know that he is also a respectedmineral collector (and in this field he is as goodas in mathematics), and a prominent photogra-pher. The author also describes Smales politicalanti-war activities, and informs us also about hisadventurous trips, such as sailing to theMarquesas.

This is the first biography written by S.Batterson, but in many respects it is a master-piece. (jiva)

M. B. Bekka and M. Mayer, Ergodic Theoryand Topological Dynamics of Group Actionson Homogeneous Spaces, London MathematicalSociety Lecture Note Series 269, CambridgeUniversity Press, Cambridge, 2000, 200 pp.,£24.95, ISBN 0-521-66030-0The book is intended as an introduction toergodic theory, with emphasis on two types ofdynamical system. The geodesic flows on theunit tangent bundle of a locally symmetric spaceand unipotent actions on homogeneous spaces.

The book is well organised and graduallydevelops the theory in six chapters. In Chapter

RECENT BOOKS

EMS Maarch 200236

Recent booksRecent booksedited by Ivan Netuka and Vladimír Sou³ek

I, we find an introduction and some classicalexamples and results from ergodic theory,including von Neumanns ergodic theorem onstrong mixing. Geodesic flows form the maintopic of Chapter II: the chapter begins with ashort section on hyperbolic geometry and geo-desic flows on Riemannian structures are thenstudied. The vanishing theorem of Howe andMoore is presented in Chapter III, together withMoores ergodicity theorem and mixing of allorders arising as a strengthening of strong mix-ing. Horocycle flows in Chapter IV are studiedfor finite-area surfaces covered by the hyperbol-ic plane: Hedlunds minimality theorem is amain result of this chapter. Chapter V intro-duces Siegel sets and their applications to lat-tices in n-dimensional Euclidean spaces. In thelast chapter, treating Oppenheims conjecture,there is an application to number theory.

This book can be used as a guide to modernergodic theory and dynamics. It can be used bygraduate students and by researchers in differ-ent areas, since the contents of the book rangefrom elementary results to modern theories.The background needed to understand thebook is a familiarity with elementary resultsfrom functional analysis, measure theory andLie theory. (dh)

R. A. Bertlmann, Anomalies in Quantum FieldTheory, International Series of Monographs onPhysics 91, Oxford University Press, Oxford, 2000,566 pp., £29.95, ISBN 0-19-850762-3 An anomaly in field theory means a violation ofclassical symmetry at the quantum level.Anomalies play a key role in modern quantumfield theory and they have been studied inten-sively since the late-1960s. Although the litera-ture on this subject is enormous, a comprehen-sive monograph on anomalies has long beenmissing Bertlmanns book thus represents ahighly desirable filling of the gap.

The core of the monograph is a discussion ofthe deeper mathematical aspects of chiral andgravitational anomalies that will appeal mostlyto the mathematically oriented theoreticalphysicists specialising in quantum field theoryand elementary particle physics. It is shown, inparticular, that the techniques of modern differ-ential geometry (which are necessary in this con-text) are useful, not only as an elegant languagefor the formulation of the theory but also as apractical computational tool. In studying theseadvanced parts, the reader is greatly helped bythe introductory chapters that include somebasic material on differential geometry andtopology and make the book fairly self-con-tained. The detailed discussion of the mathe-matical aspects tends to restrict the exposition ofthe physical applications of anomalies; on theother hand, the whole subject is so vast that aone-volume monograph can hardly be fullyexhaustive.

Bertlmanns book can be warmly recom-mended to Ph.D. students, lecturers andresearchers working in the quantum field theoryand mathematical physics, since its contents areunique within the existing literature and cover,in an essential way, the development of modernmethods in this area. (jho)

M. Bonk, J. Heinonen and P. Koskela,Uniformizing Gromov Hyperbolic Spaces,Astérisque 270, Société Mathématique de France,Paris, 2001, 99 pp., FRF 150, ISBN 2-85629-098-1The unit disc U in the complex plane can beequipped with two natural geometries: theEuclidean one, and hyperbolic geometry, whichforms on U the structure of a completeRiemannian manifold of constant negative cur-vature. This is a model case of a much more gen-eral situation that is studied here.

Given a locally compact, rectifiably connect-

ed non-complete metric space, it is possible tointroduce on it a suitable quasi-hyperbolic dis-tance. Roughly speaking, if we pass from the ini-tial metric to the quasi-hyperbolic distance, uni-form spaces become Gromov hyperbolic; con-versely, special conformal deformations of themetric of a Gromov hyperbolic space leads to auniform metric. If we compose these two modi-fications, the initial and final spaces belong tothe same quasi-similarity class. Numerous fur-ther results on Gromov hyperbolic spaces areestablished in the book. The Gehring-Haymantheorem is generalised to this framework.Loewner spaces are investigated, their definitionbeing based on the concept of the modulus of afamily of curves. Planar Gromov hyperbolicspaces are characterised, and a partial charac-terisation is also given in higher dimensions.Quasi-conformal homeomorphisms of Gromovhyperbolic spaces of bounded geometry arestudied. A description of the Martin boundary ofa Gromov hyperbolic domain establishes a linkwith potential theory.

This book is an original research work withmany deep and interesting results. It provides awell-written contribution to the geometric theo-ry of metric spaces. It is a favourite and topicaltheme to recognise which results can be gener-alised from Euclidean spaces to spaces with amore complicated geometry, and to find meth-ods that could be fruitful in this framework. Thisresearch has many applications to concreteproblems on manifolds and more generalspaces. (jama)

J. A. Buchmann, Introduction to Cryptography,Undergraduate Texts in Mathematics, Springer, NewYork, 2001, 281 pp., DM 69, ISBN 0-387-95034-6This book describes many of the well-knownsymmetric and public-key cryptosystems,together with the necessary mathematics, in away that is accessible to students with a limitedmathematical background.

The first quarter of the book is devoted todefinitions of basic mathematical structures thatare needed in modular arithmetics, the associat-ed basic algorithms (extended Euclidean algo-rithm, fast exponentiation), and the analysis ofthese algorithms and of basic modular opera-tions with respect to their computational cost.Other mathematical concepts appear in thebook later, always in connection with a cryp-tosystem. Block ciphers are associated with per-mutations, affine ciphers with matrices and lin-ear maps, and the Vernam one-time pad with adiscussion of probability notions, includingShannons theorem on perfect secrecy. The partabout symmetric cryptosystems concludes with athorough exposition of the DES algorithm.

The second half of the book is concernedwith public key encryption, including the con-cepts of digital signature, cryptographic hash-functions, identification, and certificationauthorities. RSA cryptosystems, Rabin encryp-tion, Diffie-Hellman key exchange and ElGamalencryption are all described in detail, includingsome discussion of the prime number genera-tion (Carmichael numbers, Miller-Rabin test),factoring (p1 method, quadratic sieves) and thediscrete logarithm problem (the Shanks, Pollardand Pohlig-Hellman algorithm).

This book retains the form of a mathematicaltext, with statements of theorems and proofs,but its main purpose seems to be to give a gen-eral and reasonably elaborated understandingof basic cryptographic notions. From this point,it makes sense that a several concepts are men-tioned without being really explained (such aspseudo-random numbers, class groups andnumber field sieves). There is also no attempt toformalise the concepts of algorithm complexity.However, in this and other cases, the reader isreferred to appropriate sources. The book

serves well as a first encounter with cryptogra-phy. (ad)

E. Cohen, R. F. Riesenfeld and G. Elber,Geometric Modeling with Splines. AnIntroduction, A. K. Peters, Natick, 2001, 616 pp.,US$59, ISBN 1-56881-137-3The authors present a broad base of fundamen-tally important techniques for curve and surfacerepresentations in computer-aided modelling,with a focus on their applications in design.Balancing mathematical rigour and broadapplicability, the authors show how theoreticalproperties can be used to derive practical algo-rithms. The book offers a thorough study ofapplications of splines in general, and B-splinesin particular, to the domain of geometric mod-elling.

The first two chapters contain backgroundmaterial. The next eleven chapters (conic sec-tions, differential geometry for space curves,Bézier curves and Bernstein approximation, B-splines curves, spline spaces, differential geom-etry for surfaces and surface representations)could form the basis for a one-semester intro-ductory class. A two-semester class wouldinclude most of the remaining chapters of thebook (data fitting with B-splines, fitting surfaces,modelling with B-spline surfaces, subdivisionand refinements for splines, modelling of otherpolynomial bases for interpolation, otherderivations of B-splines, set operations to effectmodelling, model data structures, subdivisionsurfaces and higher-dimension tensor productsof B-splines). The chapters conclude with exer-cises to be solved.

This is a nicely written book of great value forstimulating active work by students. In particu-lar, it can be strongly recommended as anundergraduate or graduate text, and as a com-prehensive source for a self-study. (knaj)

B. Conrad and K. Rubin (eds.), ArithmeticAlgebraic Geometry, IAS/Park City MathematicsSeries 9, American Mathematical Society, Providence,2001, 569 pp., US$75, ISBN 0-8218-2173-3 This book consists of lecture notes from the1999 Graduate Summer School (and from thecorresponding Mentoring Program for Womenin Mathematics, MPWM) of the IAS/Park CityMathematics Institute. The lecture courses werecentred around topics related to A. Wiless workon modular elliptic curves the arithmetic ofelliptic curves, modular forms and Galois repre-sentations.

The lectures by J.P. Buhler provide an intro-duction to these topics, essentially withoutproofs. Those by A. Silverberg focus on openquestions in the arithmetic of elliptic curves andabelian varieties (rational torsion points, ranksof groups of rational points, the conjecture ofBirch and Swinnerton-Dyer, the ABC-conjectureand its variants). The lectures by K.A. Ribet(written jointly with W.A. Stein) are devoted toSerres conjecture on the modularity of oddGalois representations ρ: Gal (cl(Q) /Q) → GL2(cl(Fk)). The weak Serre conjecture states that ρcomes from a modular form f; while the strongconjecture specifies the exact weight and level off. The lectures sketch proofs of various results ofthe form weak conjecture implies strong one the weight optimisation (Edixhoven) and thelevel optimisation (Ribet et al.; this result pro-vides a link between modularity of elliptic curvesand Fermats last theorem). The lectures of F.Q.Gouvêa concentrate on deformation of Galoisrepresentations. The first six lectures inspiredby B. Mazurs earlier accounts develop thegeneral theory, while the remaining two lecturessketched the (still mainly conjectural) links to p-adic families of modular forms. The lectures ofR. Greenberg treat Iwasawa theory of ellipticsurves, with emphasis on its algebraic aspects:

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variations of Mordell-Weil groups and of analyt-ic ranks in towers of number fields; Selmergroups, Λ-modules and Mazurs ControlTheorem. Two lectures by J. Tate summarisebasic properties of Galois cohomology groups.Appendices by B. Conrad and K. Buzzard, andby M. Dickinson, T. Weston and M. Emerton, tothe articles by Ribet and Stein, and Gouvêa, con-tain several technical results alluded to in themain text. The articles by W.-C. W. Li and N.Yui are based on their lectures at MPWM. Listates basic results on modular forms, while Yuidiscusses the arithmetic of L-functions of Calabi-Yau 3-folds.

The book is aimed at Ph.D. students in num-ber theory. It begins at a fairly introductorylevel, but gives a good overview of the subjectand proceeds naturally to more technicalaspects of the theory. An attractive feature of thebook is the presence of many exercises for stu-dents. (jnek)

J. F. Davis and P. Kirk, Lecture Notes inAlgebraic Topology, Graduate Studies inMathematics 35, American Mathematical Society,Providence, 2001, 367 pp., US$55, ISBN 0-8218-2160-1This book is based on a second-year course onalgebraic topology and the authors presentmaterial which, in their opinion, every youngtopologist should know. The second aim of theauthors is to provide enough information fromalgebraic topology for people interested in geo-metric topology.

In order to make the book self-contained,the authors present three chapters on basic factsfrom homological algebra. The first chapterconsists of a brief introduction to chain com-plexes, homology and cohomology, with appli-cations to CW-complexes, simplicial and singu-lar theory. The second chapter gives anoverview of homological algebra, including uni-versal coefficient theorems. Chapter 3 is devot-ed to products in the homology and cohomolo-gy, including the Künneth formulas and thePoincaré duality theorem.

The theory of fibre bundles is explained inthe fourth chapter, which is also the startingpoint of an advanced course. Both principal andassociated bundles are introduced here, and theÈech cohomology is mentioned as well. Thehomology and cohomology of spaces with localcoefficients are presented in Chapter 5.Fibrations, cofibrations and homotopy groupsare studied in the sixth chapter: this chapteralso presents a brief introduction into homotopytheory, ending with the Hurewicz andWhitehead theorems.

In the next part of the book, obstruction the-ory and Eilenberg-MacLane spaces, bordism,spectra and generalised homology are dis-cussed. At the end of the book, spectralsequences are defined and explained, and theirapplications to several problems in algebra andalgebraic topology are presented; for example,there are applications to computations of homo-topy groups of spheres, cohomology operationsand construction of bordism invariants. Thefinal chapter is devoted to a study of simple-homotopy theory and torsions, such as theWhitehead and the Reidemeister torsion andtheir applications. There are many exercisesand comments in the book, which complementthe material, as well as suggestions for furtherstudy, presented in the form of projects.

The book is a nice advanced textbook onalgebraic topology and can be recommended toanybody interested in modern and advancedalgebraic topology. (jbu)

A. Dijksma, M. A. Kaashoek and A. C. M. Ran(eds.), Recent Advances in Operator Theory,Operator Theory Advance and Applications 124,

Birkhäuser, Basel, 2001, 558 pp., DM 260, ISBN3-7643-6573-0A conference held at Groningen (Netherlands)in December 1998 was organised on the occa-sion of the 70th birthday of Israel Gochberg,who is one of the initiators of the series ofInternational Workshops on Operator Theoryand its Applications (IWOTA), to which the con-ference belonged. This volume is a selection of35 papers in operator theory, related to lecturespresented at the meeting.

Most of the papers contain rather long intro-ductions that can be used by non-experts as aguide to a current state of research in the theo-ry of linear operators in Hilbert spaces. The arti-cles deal with analytic operator functions, inter-polation and extension problems, dilation andcommutant lifting theorems, several problemsconnected with control theory, Hilbert functionspaces and spaces with indefinite metrics. Thereare also applications to partial differential equa-tions (spectra of elliptic operators, scatteringtheory, multiplier theorems and R-bounded-ness).

A short description of I. Gochbergs mathe-matical work (by M.A. Kaashoek) and a com-plete list of his publications are added. (jmil)

H. M. Enzensberger, Drawbridge Up:Mathematics - A Cultural Anathema, A. K. Peters,Natick, 1999, 47 pp., US$9.95, ISBN 1-56881-156-XThis book contains the bilingual version(German and English) of an address given bythe author at the 1998 International Congress ofMathematicians in Berlin. The first edition wasin paperback form in 1999: a review of it can befound in this Newsletter, No. 34, Dec 1999, p.37.(vs)

T. Friedrich, Dirac Operators in RiemannianGeometry, Graduate Studies in Mathematics 25,American Mathematical Society, Providence, 2000,195 pp., US$34, ISBN 0-8218-2055-9This book is a nice introduction to the theory ofspinors and Dirac operators on Riemannianmanifolds. It consists of an algebraic part, intro-ducing Clifford algebras, spin groups and spin-ors, a topological part, discussing existence anda classification of spin structures on compactRiemannian manifolds, and an analytical part,where the Dirac and the twistor operators andtheir properties are studied in detail. Specialattention is paid to eigenvalue estimates and tosolution spaces of special spinorial field equa-tions, such as Killing spinors and twistor spinors.The main text is completed by two appendicesthat are also of special interest and containmaterial that is needed earlier in the book.Appendix A contains a nicely written descriptionof the Seiberg-Witten theory of invariants for 4-dimensional manifolds, one of the main topicsin 4-dimensional manifold theory in recentyears. Appendix B is devoted to the theory ofprincipal bundles and connections, their reduc-tions and holonomy theory.

This book can be strongly recommended toanybody interested in the theory of Dirac andrelated operators. (jbu)

P. G. Goerss and J. F. Jardine, SimplicialHomotopy Theory, Progress in Mathematics 174,Birkhäuser, Basel, 1999, 510 pp., DM 118, ISBN3-7643-6064-XSince the last monograph on simplicial homo-topy theory appeared more than twenty-fiveyears ago, one of the aims of this monograph isto fill this gap, at least partially. Quillens workon closed model structures, which now belongsto the foundations of simplicial homotopy theo-ry, is one of the main subjects of this mono-graph. However, the monograph starts from thevery beginning, from the simplicial sets, and no

prerequisites from simplicial homotopy theoryare needed. More precisely, this book should beaccessible for a second-year graduate student.

After so many years of intensive develop-ment, we cannot expect the monograph to coverall subjects in the field. It is oriented mostlytowards algebraic topology, while other fields ofapplications, such as homological algebra, alge-braic geometry, number theory and algebraic K-theory are not included. Nonetheless, anotheraim of the monograph is to provide specialists inother fields, intending to use simplicial homo-topy theory in their own fields, with a necessaryworking knowledge of the theory. Having this inmind, the authors have prepared the list of ref-erences in such a way that it gives a basic orien-tation in the above-mentioned fields of applica-tion.

But the main aim is to gather together oldand new results and serve specialists in the fieldof simplicial homotopy theory. It is nice that oldresults are sometimes presented in a new form,with a deeper insight and surprising relations.The authors have decided not to include exer-cises or problems; instead, they saturate the textwith many interesting and inspiring examples.The whole monograph is carefully and nicelywritten, and for experts it is quite indispensable.For its quality and importance it should beincluded in every mathematical library. (jiva)

H. Grassmann, Extension Theory, History ofMathematics 19, American Mathematical Society,London Mathematical Society, Providence, 2000,411 pp., US$75, ISBN 0-8218-2031-1This book is an English translation ofGrassmanns Ausdehnungslehre, which was pub-lished in Berlin in 1862. The translation byLloyd C. Kannenberg (who has also translatedPeanos Calcolo geometrico secondolAusdehnungslehre di H. Grassmann, preceduto delleoperazioni della logica deduttiva, Birkhäuser,Boston, 2000) is based on HermannGrassmanns Gesammelte mathematische undphysikalische Werke (Teubner, Stuttgart, Leipzig,1896).

The German mathematician HermannGünter Grassmann (1809-77) developed a circleof ideas relating multi-dimensional geometry,linear algebra and vector analysis. The first edi-tion of his Extension Theory appeared in Leipzigin 1844 under the name Die linealeAusdehnungslehre, ein neuer Zweig der Mathematik.In 1861, the book was essentially rewritten andextended, and the author skipped unnecessaryphilosophical parts. The second edition wasprinted under the name Die Ausdehnungslehre.New material not included in the first editioncovers, for example, a development of the innerproduct, the concept of angle, Grassmanns the-ory of functions and Grassmanns contributionsto the Pfaff problem.

This book contains Grassmanns Extensiontheory (325 pp.), the Editorial Notes (59 pp. fromGrassmanns Gesammelte Werke, 1896),Supplementary Notes (8 pp.) and Subject Index(13 pp.). Grassmanns classical work can bewarmly recommended to mathematicians and tohistorians of mathematics as a source ofGrassmanns mathematical ideas. (jbe)

J. E. Graver, Counting on Frameworks.Mathematics to Aid the Design of RigidStructures, Dolciani Mathematical Expositions 25,Mathematical Association of America, Washington,2001, 180 pp., £23.95, ISBN 0-88385-331-0This is a nice little introduction to combinatori-al rigidity theory by an experienced author. Avery careful and accessible exposition (some-times even a little slow for someone used toreading mathematics) starts from simple exam-ples and ideas and proceeds to a theory of therigidity of frameworks made of rods in dimen-

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sions 1, 2, and 3. Several advanced theoremsand their proofs are presented, or at leastsketched, and further reading is suggested forthe more advanced topics. The main theme iscomplemented by sections concerning history,geodesic domes, linkages and tensegrity frame-works (made of rods and cables).

While some calculus and linear algebra areassumed, the basic notions and results of graphtheory are carefully explained. (jmat)

H. Hauser, J. Lipman, F. Oort and A. Quirós(eds.), Resolution of Singularities, A ResearchTextbook in Tribute to Oskar Zariski, Progress inMathematics 181, Birkhäuser, Basel, 2000, 598 pp.,DM 168, ISBN 3-7643-6178-6The basic question treated in the book is: givena variety X, determine a subvariety Z of X suchthat blowing up X in Z resolves the singularity ofX. The book is a report on recent results andproblems concerning this problem. It is dedicat-ed to the memory of the well-known algebraicgeometer Oskar Zariski, who created fundamen-tal parts of the theory.

The book divides into two parts. Part I con-sists of extended manuscripts of lectures givenat a Working Week on Resolutions ofSingularities, at Obergurgl in Tirol, Austria, inSeptember 1997. It contains contributions by D.Abramovich and F. Oort (Alternations and reso-lution of singularities), J. M. Aroca (Reductionof singularities for differential equations, andPuiseux solutions of singular differential equa-tions) and S. Encinas and O. Villamayor (Acourse on constructive desingularisation andequivariance).

Part II contains articles written especially forthis volume: there are fifteen contributions alto-gether. We mention just a few, by G. Bodnar andJ. Schicho (A computer program for the resolu-tion of singularities), B. van Geemen and F.Oort (A compactification of fine moduli space ofCurves), G. Muller (Resolution of weightedhomogeneous surface singularities) and M.Vaquie (Valuations); in these articles, specialrelated questions are discussed. There are alsoshort communications describing the life andwork of O. Zariski by J. Lipman, and an inter-esting historical account by H. Hauser on theresolution of singularities, in the period 1860-1999. (jbu)

D. J. Hurley, and M. A. Vandyck, Geometry,Spinors and Applications, Springer and PraxisPublishing, London, 2000, 369 pp., DM 179, ISBN1-85233-223-9The main topics in this book are covariant deriv-atives of spinor fields and their use in theoreti-cal physics (Newtonian mechanics, electromag-netism, gravitation). The first two parts of thebook present the necessary prerequisites.

In the first part, standard linear algebra tools(vector spaces and their duals, tensors, exterioralgebra, Clifford algebras) are developed indetail. In the second part, basic notions ofsmooth manifolds, tangent spaces, vector fields,Lie derivatives, connections and covariant deriv-atives are explained, with special parts devotedto the Riemannian case, Lie groups and the cor-responding Lie algebras. These notions are usedfor a description of fibre bundles and vectorbundles, and connections and covariant deriva-tives on them. The main part of the book isdevoted to a description of spinor fields on(pseudo)-Riemannian manifolds and covariantderivatives acting on them (not necessarily com-patible with the metric structure). Special atten-tion is paid to the Minkowski case.

The book is clearly written for theoreticalphysicists, but uses a lot of standard coordinate-free mathematical tools. The notation employedis a mixture of those used in mathematics and inphysics, but should be understandable. The

book will be useful for graduate and postgradu-ate students of theoretical physics. (vs)

G. W. Johnson and M. L. Lapidus, TheFeynman Integral and Feynmans OperationalCalculus, Oxford Mathematical Monographs,Clarendon Press, Oxford, 2000, 771 pp., £90, ISBN0-19-853574-0 This is a representative monograph (770 pages)on all aspects of the mathematical theory of theFeynman integral. This elusive and formidablesubject has attracted mathematicians from itsvery beginning, and several different approach-es to the rigorous mathematical theory of theFeynman integral have appeared in the courseof the last half-century, after the heuristic con-cept of summation over all paths was formulat-ed by R. Feynman in 1949. This book sum-marises all existing approaches and explainstheir mutual relations (and, often, their equiva-lence). Much of the original work on the subjectis due to the authors of the book.

The book starts with an extensive and thor-ough introduction, as for the more specialisedthemes in the subsequent chapters. This makesthe book accessible, even for beginners. In addi-tion, many quotations of sayings by famous per-sonalities (related to the subjects treated in thebook) provide amusement for the reader.(However, some readers could find it unusualthat the same script is used in the book for boththe theorems and the remarks.)

The first part of the book (Chapters 1-13)contains, among other things, a complete treat-ment of existing approaches to the concept ofthe Feynman path integral namely, themethod of analytical continuation (in time ormass) converting the problem of Feynman inte-gral to the well-established theories of Wienerintegrals and Brownian motion, the method ofTrotter formulas employing many deep resultsfrom the theory of operator semigroups, andthe modified method, due to the authors of thebook, that replaces the exponentials in theTrotter formulas by suitable resolvent operators.(The concept of a Fresnel integral is also dis-cussed, but is postponed to the last chapter ofthe book.) It is shown that all these approaches(if applicable) coincide under reasonably gener-al conditions. The second part of the book(Chapters 14-19) is devoted to a related subject:Feynmans operational calculus for non-com-muting variables; again, this subject is explainedthoroughly from the very beginning.

To summarise, this book should serve as astandard reference for anybody interested in themathematical theory of Feynman path integralsand the related operational calculus. (mzahr)

M. Jutila and T. Metsänkylä (eds.), NumberTheory, Proceedings of the Turku Symposium onNumber Theory in Memory of Kustaa Inkeri, 1999,Walter de Gruyter, Berlin, 2001, 328 pp., DM 268,ISBN 3-11-016481-7This volume contains selected contributions by71 participants at a conference organised by theRolf Nevalinna Institute in honour of thefounder of the Finnish number theory tradition,Kustaa Inkeri (1908-97). The papers cover abroad spectrum of elementary, analytic andalgebraic number theory.

The reader will find many interesting contri-butions: the life and work of Inkeri (Metsänkyläand van der Poorten), Diophantine problems(Bugeaud and Frey, Mignotte), sieve methods(Greaves and Huxley), arithmetic functions(Haukkanen), Lucas and Pell numbers(Ribenboim and McDaniel, Strazdins),Riemann, Dirichlet, Hecke and L-series (Iviæ,Jutila, Matsumoto, Laurin, Sands), exponentialsums (Huxley and Kolesnik), summation of mul-tiple series (Dilcher, Haller), arithmetic aspectsof functional equations (Bundschuh), hypergeo-

metric and binomial series (Amou, Katsuradaand Väänänen, Matala), higher power residuesymbols (Helou), representation of primes byspecial quadratic forms (Jackson), binary addi-tive divisor problem (Meurman). The volume iscarefully prepared. (p)

W. J. Kaczor and M. T. Nowak, Problems inMathematical Analysis, II. Continuity andDifferentiation, Student Mathematical Library 12,American Mathematical Society, Providence, 2001,398 pp., USD$49, ISBN 0-8218-2050-8This book is the second volume of a series ofproblem books in mathematical analysis: thefirst appeared a year ago and others will follow.It contains three chapters and covers subjectslike limits, continuity, differentiation, and limitsand series of functions. Numerous problems arewell chosen and solutions of all of them are pro-vided. The first chapter contains 212 problems,including some on functional equations (con-nected mostly with elementary functions) andcontinuity on metric spaces, while the secondand third chapters contain 238 and 130 prob-lems, respectively.

As with the first volume, the book is of greathelp for problem seminars and also for self-study. Some problems are not new and theauthors mention some sources in the preface.Almost two-thirds of the volume are devoted tothe presentation of solutions, usually in a rela-tively detailed manner; those who know the firstvolume will probably appreciate this continua-tion.

This book can be recommended for librariesand for students. (jive)

W. M. Kantor and A. Seress (eds.), Groups andComputation III, Ohio State Univ. MathematicalResearch Institute Publications 8, Walter de Gruyter,Berlin, 2001, 368 pp., DM 248, ISBN 3-11-016721-2This collection of 23 papers presents a fairlyaccurate picture of the current trends and likelyfuture developments in computational grouptheory. While permutation groups and matrixgroups remain in the focus of the researchers,the emphasis shifts discernibly towards the moregeneral model of a black box group, introducedin 1984. The nature of this model calls for prob-abilistic algorithms (Monte Carlo, Las Vegas)that consequently appear throughout the vol-ume.

The papers can be somewhat artificiallydivided into five categories (in order of frequen-cy): group recognition, computational solutionsto classical group-theoretical problems, briefsurveys of computational group theory, theoret-ical results concerning groups and algorithms,and software documentation. The concrete top-ics range from the recognition of finite speciallinear groups and experimentation with cosetenumeration to a solution of the Andrews-Curtisconjecture and a classification of unisingulargroups. Many results are based on Aschbachersclassification of maximal subgroups of classicalgroups. References to machine computation(implemented in GAP, MAGMA, MEATAXE)are omnipresent and form a vital part of manyarguments. Although the tools for parallel com-puting have now been included in algebraicpackages (such as ParGAP), most of the algo-rithms remain non-parallel a certain target forthe future.

Computational group theory evolves dramat-ically, as is eloquently documented by theunusually high amount of cross-referencingamong the contributions to this volume.Naturally, this phenomenon is a consequence ofthe close interaction of the authors with the edi-tors, whose careful and precise work have madethe papers look almost as chapters in a bookwritten by one author. Their effort will be great-

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ly appreciated by experts and readers with someknowledge of the area. Beginners, however,must look for the preliminaries elsewhere. (ad)

J. Kigami, Analysis on Fractals, CambridgeTracts in Mathematics 143, Cambridge UniversityPress, Cambridge, 2001, 226 pp., £35, ISBN 0-521-79321-1This book contains some very important toolsfor studying the dynamical aspects of objectsmodelled by fractals, and builds the theory ofanalysis on fractals. This is a developing areaof mathematics that focuses on the dynamicalaspects of fractals, such as heat diffusion onfractals and the vibration of a material withfractal structure.

The book provides a self-contained intro-duction to the subject, starting from the basicgeometry of self-similar sets and going on torecent results, including the properties ofeigenvalues and eigenfunctions of theLaplacians, and the asymptotic behaviour ofheat kernels on self-similar sets.

Requiring only a basic knowledge ofadvanced analysis, general topology and mea-sure theory, this book will be of value to grad-uate students and researchers in analysis andprobability theory. It will also be useful as asupplementary text for graduate courses cov-ering fractals. Individual chapters containsuch topics as the geometry of self-similar sets,analysis on limits of networks, the constructionof Laplacians on P.C.F. self-similar structures,eigenvalues and eigenfunctions of Laplaciansand heat kernels. Some mathematical back-ground (self-adjoint operators, quadraticforms, semigroups, Dirichlet forms, Nashinequality and the renewal theorem) isdescribed in the Appendix. (pp)

S. Levy (ed.), The Eightfold Way. The Beauty ofKleins Quartic Curve, Cambridge UniversityPress, Cambridge, 2001, 331 pp., £19.95, ISBN0-521-00419-5The first edition of this book appeared in1999, and a review can be found in thisNewsletter, No. 39, March 2001, p.32. This isthe second unchanged paperback edition ofthe book. (vs)

J. H. van Lint and R. M. Wilson, A Course inCombinatorics, second edition, CambridgeUniversity Press, Cambridge, 2001, 602 pp.,£24.95, ISBN 0-521-00601-5In this second edition, some material has beenadded (list-colorings of graphs, the Lovászsieve, associative block designs) and there aremany new exercises. The book is unique in thevariety of topics treated, in 38 chapters onmore than 550 pages and in the large spacedevoted to non-graph-theory combinatorics.

The following list provides a brief overview,by no means exhaustive, of the areas covered:graph theory (Eulerian and Hamiltonian cir-cuits, spanning trees, Turáns theorem, Hallstheorem, Ramseys theorem, connectivity, pla-narity, squared squares, graphs on surfaces),posets (Dilworths theorem, Sperners theo-rem), permanents (the Minc and van derWaerden conjectures), Latin squares (count-ing, the Evans conjecture, the Dinitz conjec-ture, orthogonal Latin squares), enumeration(de Bruijn sequences, the Möbius function,generating functions, Bell and Stirling num-bers, Lagrange inversion, partitions, theJacobi triple product identity, Young tableaux,0-1 matrices, Pólya theory), algebraic combi-natorics (projective and combinatorial geome-tries, Gaussian numbers, q-analogues, stronglyregular graphs, difference sets, Singers theo-rem, Shannon capacity, association schemes),and designs and codes (Hadamard matrices,Paley matrices, Steiner systems, Golay codes,

Reed-Muller codes, the Bruck-Ryser-Chowlatheorem, Baranyais theorem).

This well written textbook can be highlyrecommended to any student of combinatoricsand, because of its breadth, has many newthings to tell researchers in the field also. (mk)

A. Mehlmann, The Games Afoot! Game Theoryin Myth and Paradox, Student MathematicalLibrary 5, American Mathematical Society,Providence, 2000, 159 pp., US$26, ISBN 0-8218-2121-0 Looking at the title and the format of this book,one is inevitably reminded of the well-knownThe Compleat Strategyst by J. Williams (DoverPublications, N.Y., 1986). However, this firstimpression quickly disappears after the readingof the first few pages. Mehlmanns book is noprimer in the theory of games, but a ratheradvanced treatment of different aspects of thetheory of games and its applications. Variousconcepts and problems are discussed from dif-ferent points of view and illustrated by means ofparables from history, mythology and literatureof fiction. These features make the book a fasci-nating, entertaining and enlightening reading.

In the authors words, the book is intendedas a light-hearted excursion into the world ofstrategic calculation. However, to enjoy thisexcursion fully, the reader should depart on itequipped with some basic knowledge of the fun-damentals of game theory and a fairly broadgeneral cultural background. (jmach)

R. A. Minlos, Introduction to MathematicalStatistical Physics, University Lecture Series 19,American Mathematical Society, Providence, 2000,103 pp., US$24, ISBN 0-8218-1337-4This is a book on rigorous statistical physics.The author is one of the co-founders and lead-ing figures of this important, and (after 40 yearsof development) still flourishing field ofresearch. The subject of the book the theoryof interacting multicomponent systems lies onthe border between mathematics and other sci-ences. The greatest impact came from physics,not only through phenomena like phase transi-tions but also some important methods devel-oped originally by theoretical physicists. Thesemethods, like the method of expansions, werelater converted (notably also by the author ofthis book) into important technical tools of puremathematics. On the other hand, anotherimportant and traditional tool of mathematicalstatistical mechanics is probability theory.

In the 103 pages of this book, the authorpresents a concise introduction to the subject.In Part I he discusses basic concepts (phasespace, dynamics, statistical ensembles) andbasic examples (ideal gas, lattice gas) of the the-ory. He then gives a concise explanation ofimportant statistical ensembles (micro-canoni-cal, canonical, grand-canonical) and of theirmutual relations. He then explains, in Part II,the method of correlation functions (expan-sions) based on the use of Kirkwood-Salsburgequations. Finally, he discusses various thermo-dynamical potentials entropy, pressure, freeenergy, etc. Part III deals with phase transi-tions. The author explains the famous Peierlsmethod of contours, not only for the simplestcase of the Ising model, but also in detail for itsmore sophisticated form, the Pirogov-Sinai the-ory. Finally, in an epilogue, he adds a short dis-cussion of Wulff droplets and the rougheningtransition.

There is a vast journal literature on the sub-ject of this book, but relatively few standard ref-erence texts. This new textbook will surely findits place among existing monographs (Ruelle,Sinai, Georgii, Simon, etc.) that do not usuallycover every important topic or are directedtowards a more specialised reader. (mzahr)

C. J. Mozzochi, The Fermat Diary, AmericanMathematical Society, Providence, 2000, 196 pp.,US$29, ISBN 0-8218-2670-0As the title indicates, this book is an eye-witnessaccount of the events leading to the final solu-tion of Fermats Last Theorem. The authorattended each of the lectures that are nowlabelled as milestones on the way leading to thecorrect solution of this problem, which becameone of the most famous ones in mathematics. Hetook notes during the lectures, read and sum-marised the reports in the newspapers and jour-nal, and took more than thousand photographsduring and after the lectures and the connectedsocial events.

This material forms the backbone of thereport contained in the book. It is written in alively style and is easy to read and as such, it canbe recommended to those of us who were notlucky enough to have an opportunity to followthese events personally. With its many interest-ing facts, often unattainable to those not direct-ly engaged in the story, its many personal quo-tations, and pictures of personalities involved,the book will certainly be an important sourcefor historical details surrounding the proof forcontemporaries and those born later. (p)

H. Niederreiter and C. Xing, Rational Pointson Curves over Finite Fields. Theory andApplications, London Mathematical Society LectureNote Series 285, Cambridge University Press,Cambridge, 2001, 245 pp., £27.95, ISBN 0-521-66543-4Many important results from number theoryand geometry have their roots in the propertiesof algebraic curves. This book focuses on alge-braic curves over finite fields and their functionfields, with a special emphasis on applications.

The first three chapters cover the necessarybackground on algebraic number fields, classfield theory and global function fields for thefollowing core chapters. In the first two chaptersthe reader finds how to construct global functionfields with many rational places, and meetsresults about the asymptotic behaviour of thenumber of rational places of global functionfields.

The book mostly reflects recent results, andso the application chapters discuss methods ofalgebraic geometry in coding theory (Goppa,NXl and XNL codes), applications to cryptogra-phy (almost perfect sequences, perfect hashfunctions and low-discrepancy sequences).Because of the carefully selected contents andlucid style, the book can be warmly recommend-ed to mathematicians interested in the above-mentioned topics or in algebraic curves overfinite fields with many rational points. (p)

W. F. Pfeffer, Derivation and Integration,Cambridge Tracts in Mathematics 140, CambridgeUniversity Press, Cambridge, 2001, 266 pp., £45,ISBN 0-521-79268-1This book is devoted to the theory of non-absolutely convergent integrals in Euclideanspaces, and was written by one of the leadingspecialists in this field. It is natural to askwhether there exists a generalisation of theLebesgue integral such that the Gauss-Greentheorem in Rn holds for each differentiable vec-tor field v and suitable sets A, if the integral overA of div v is taken in the sense of this generalisedintegral. If we also need good properties of thegeneralised integral (in particular, its rotationinvariance), the problem cannot be solved by adirect generalisation of the Denjoy-Perron inte-gral. However, in the last twenty years, severalsolutions have been found; they use the idea ofthe Kurzweil-Henstock (Riemann type) defini-tion of the Denjoy-Perron integral.

The solution presented in this book is basedon the theory of (finitely) additive set functions,

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defined on the family of all bounded BV sets inRn; such set functions, which are continuous withrespect to a suitable topology, are calledcharges. In the book, a deep theory of deriva-tives and variations of charges is presented.Using a type of variation, the important class ofAC* charges is defined. The basic definition ofthe R-integral is a descriptive one, and is basedon the notion of the indefinite R-integral.Roughly speaking, the indefinite R-integral of fis an AC* charge for which DF(x) = f(x) foralmost all x, where DF(x) is a suitable type ofderivative. An equivalent Riemann-type defini-tion of the R-integral is also given (hence the let-ter R). Using the R-integral, a very generalGauss-Green theorem can be proved, and theauthor explains how it can be extended to theStokes theorem on Lipschitz manifolds. In thefinal chapter, the R-integral is extended to theGR-integral, which has even better propertiesthan the R-integral.

The book is well organised and is written ina precise and lucid style. It can be recommend-ed to anybody interested in the theory of non-absolutely convergent integrals, and has a solidbackground in graduate level analysis. (lz)

J.-P. Pier, Mathematical Analysis During the20th Century, Oxford Univesity Press, Oxford,2001, 428 pp., £59.50, ISBN 0-19-850394-6This book is devoted to the history of some partsof mathematical analysis, including probabilityand algebraic geometry in the 20th century.While the period 1900-50 is treated in certaindepth, the evolution from 1950 to 2000 is char-acterised by representative achievements. Thebook contains many original quotations (withEnglish translations) and brief expositions ofresults chosen to illustrate the main ideas andtrends.

The chapters contain texts on general, alge-braic and differential topology, integration andmeasure, functional and harmonic analysis, Liegroups, the theory of functions and ODEs andPDEs. The text occupies approximately 350pages, numerous references take another 60pages, and two Indexes and a List of Symbolstake about 20 pages. It will be a valuable sourcebook for analysts interested in the history of themain ideas of analysis, as well as for others want-ing to know about developments in other fields.A certain familiarity with the material includedwill be of great help. The book can be recom-mended to mathematical libraries, researchersand students. (jive)

V. P. Pikulin and S. I. Pohozaev, Equations inMathematical Physics. A Practical Course,Birkhäuser, Basel, 2001, 206 pp., DM 196, ISBN3-7643-6501-3This book demonstrates the basic methods forsolving classical linear problems in the mathe-matical physics of elliptic, parabolic and hyper-bolic types. In particular, methods of conformalmappings, Fourier analysis and Greens func-tions are considered, as well as the perturbationand integral transformation methods, amongothers. Each chapter contains concrete exam-ples with a detailed analysis of their solution,and ends with problems for independent studyand answers to them. This handbook isaddressed to students of technology instituteswhere a course on mathematical physics of rela-tively reduced volume is offered, as well as toengineers and scientists. (kn)

Yu. V. Prokhorov and V. Statulevièius (eds.),Limit Theorems of Probability Theory, Springer,Berlin, 2000, 273 pp., DM 169, ISBN 3-540-57045-4 This reference book is a collection of research-level surveys covering different results on cer-tain topics of probability theory. All parts of the

book are self-contained and each special topiccan be studied independently.

The book consists of five chapters on limittheorems in probability theory, written by lead-ing researchers in the area. The classical part oflimit theorems is presented by V. V. Petrov inChapter I. Central limit theorems, laws of largenumbers, the Berry-Esséen inequality, and thelaw of the iterated logarithm are covered in thischapter. V. Bentkus et al. wrote Chapter II, con-taining the problem of accuracy of Gaussianapproximation for distribution on infinite-dimensional Banach spaces. Chapter III, writtenby J. Sundoklas, treats the asymptotic behaviourof sums of weakly dependent random variablesand its approximation by the normal distribu-tion. In Chapter IV, homogeneous Markovchains and their central limit theorem is stud-ied; this chapter is written by P. Gudynas. Thefinal chapter, by L. Saulis and V. Statulevièius, isdevoted to limit theorems on large deviation.

This book should be at hand for any special-ist on asymptotic methods in probability and sta-tistics, and can also serve as a basic reference forgraduate and Ph.D. students of stochastics. (dh)

L. Schwartz, A Mathematician Grappling withHis Century, Birkhäuser, Basel, 2001, 490 pp.,DM 68, ISBN 3-7643-6052-6Laurent Schwartz is one of the most distin-guished mathematicians of the 20th century. Hisautobiography can be considered, apart fromother things, as a history of mathematics fromthe 20th century, and partly also of the centuriesbefore. He describes the development of mathe-matical thinking towards its current level ofexactness. He was for a certain time a memberof the Bourbaki group, which contributed sub-stantially to this development. Thanks to hiscooperation with many mathematicians all overthe world, he has been able to give interestingcomments on circumstances connected with sub-stantial mathematical discoveries. In particular,he speaks about his most important discovery,distribution theory, which has many applica-tions in both pure and applied mathematics.

Schwartz has been, however, not only a math-ematician. Besides his scientific work and apartfrom his teaching activities, he was also veryactive in the social and political arena. He was aconvinced Trotskyist. Thus, the reader will findcomments on significant events of the 20th cen-tury, mainly on both the world wars, on politicaldevelopment in the USSR, and so forth.Everything is based, if not on his personal mem-ories, on direct evidence from his numerousfriends from all over the world. He has alwaysfought for peace and has opposed localisedwars, especially in Algeria and Vietnam, wherehe also lived for some time. Writing a bookdescribing so many particular events precisely iswitness to the authors prodigious memory. Heremarks that he made notes to refresh his mem-ory only in his advanced age. The book is attrac-tive and can be highly recommended to anyreader intersted in the subject. (jjel)

R. Y. Sharp, Steps in Commutative Algebra, sec-ond edition, London Mathematical Society StudentTexts 51, Cambridge University Press, Cambridge,2000, 355 pp., £17.95, ISBN 0-521-64623-5This book is meant as a tool for an undergrad-uate student with some knowledge of polynomi-als and linear algebra to grasp the basic notionsof structural commutative algebra. The self-professed goal of the book (see the preface tothe first edition) is to close the gap betweenbooks on basic algebra (which include topicslike unique factorisation in Euclidean domains)and existing books on commutative algebra thatrequire much deeper experience and sophisti-cation. This book seems to assume that thereader has no problems in doing even quite

complex calculations with polynomials, but mayhave nearly no experience with abstract struc-tural mathematics. This can be observed in thecare with which the author explains notionsrelated to factorisation, both in the context ofring ideals and submodules.

In addition to the basic material, the firsthalf of the book is concentrated around the pri-mary decomposition of ideals, the structure ofcommutative Noetherian rings and the struc-ture of modules over principal ideal domains.As an application, the author derives the canon-ical forms of square matrices, and presentssome applications to field theory, up to tran-scendental extensions. The closing chapters(about 100 pages) deal with integral depen-dence, affine algebras over fields, dimensiontheory, regular sequences (and grade) andCohen-Macaulay rings. The latter two chaptersdid not appear in the first edition, and consti-tute the main difference between the two edi-tions (beyond the corrections of misprints,which are now very few). The author has suc-ceeded in keeping the context within the self-imposed limits there is no reference to thetensor product, categories are touched on onlymarginally, and the exposition is careful andclear. A patient reader can learn a lot, withouthaving to leave the firm ground of set structuresthat are manipulated only in a way that makesit easy to keep in mind the role of individualelements. (ad)

P. N. de Souza and J.-N. Silva, BerkeleyProblems in Mathematics, second edition, ProblemBooks in Mathematics, Springer, New York, 2001,535 pp., DM 73,83, ISBN 0-387-95207-1This is the second and enlarged edition of aproblem book for first-year Ph.D. students inmathematics. A review of the first edition can befound in this Newsletter, No. 30, Dec 1998, p.41.The new edition contains about 150 additionalproblems and 250 new solutions. (vs)

G. Tenenbaum and M. M. France, The PrimeNumbers and their Distribution, StudentMathematical Library 6, American MathematicalSociety, Providence, 2000, 115 pp., US$17, ISBN0-8218-1647-0This is an English translation of the French edi-tion, first published in 1997 as a volume in apaperback encyclopaedia containing about3500 titles, each of them limited to 128 pages;this limitation immediately implies bounds forsuch an extensive field as the theory of primenumbers. Nevertheless, the authors have suc-ceeded in writing an interesting volume thatcan be recommended to students. The readerwill find basic introductory elementary resultssuch as the Chebyshev or Mertens theorem andBruns sieve applied to the twin prime conjec-ture. The book also contains a complete andself-contained elementary proof of the primenumber theorem in Daboussis version of 1984.The middle chapter, on the stochastic distribu-tion of prime numbers reflects the authorsdecision to describe various aspects of primenumber theory from the point of view of ran-domness, giving to the book a specific charm. Italso contains an introduction to Dirichlet andSiegel-Walfish theorems on primes in arith-metical progressions, Siegel zeros and a discus-sion of consequences of Cramers probabilisticmodel of the distribution of primes generatedby the measure induced by the reciprocal of thelogarithmic function. Finally the reader canfind the basics of uniform distribution.

This book can be read by anyone with a min-imal knowledge of number theory and somecalculus skills. (p)

G. Tian, Canonical Metrics in Kähler Geometry,Lectures in Mathematics ETH Zürich, Birkhäuser,

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EMS December 2001 41

Max-Planck-Institut für Mathematik in den NaturwissenschaftenMax Planck Institute for Mathematics in the Sciences

At the Max Planck Institute for Mathematics in the Sciences in Leipzig(Germany), we have an open position for a postdoc in the field of

Mathematical Modelling of Cognitive Systems.

Applicants should be able to build upon a solid education in mathe-matics or physics in order to develop and analyze formal models, forexample neural networks, that lead to new insights about informationprocessing and cognitive structures. The work will take place in anopen interdisciplinary group at a research institute with a strong back-ground in mathematics and with many and diverse international con-tacts. Collaborations with researchers at the University of Leipzig orother institutions are possible.

The position is offered for two years, with the possibility of an exten-sion in case of mutual interest. The beginning date is flexible.

Handicapped applicants will be given preference in case of equal qual-ification. The Max Planck Society as the employer aims at increasingthe number of female scientists in fields where underrepresented.Therefore, women are particularly encouraged to apply.

Please send your application to

Jürgen JostMax-Planck-Institut für Mathematik in den Naturwissenschaften

Inselstrasse 22, D-04103 Leipzigjost@mis.mpg.de

Basel, 2000, 1000 pp., DM 38, ISBN 3-7643-6194-8In recent years, uniformisation theory of canon-ical Kähler metrics in higher dimensions hasbeen developed in complex differential geome-try. One of its applications is the use of Calabi-Yau spaces in superstring theory. The presentedmonograph is a systematic and self-containedintroduction into the theory of canonical Kählermetrics on complex manifolds.

The following topics are described in the firstpart of the book: Kähler metrics and their cur-vature tensor, the space of Kähler metrics on agiven manifold, the Calabi functional, andextremal metrics and uniformisation of Kähler-Einstein manifolds. In the second part a holo-morphic invariant for Kähler manifolds (calledthe Calabi-Futaki invariant) is introduced andits properties are described. Special attention ispaid to the scalar curvature of Kähler metrics inthe corresponding symplectic geometry, and theCalabi-Yau theorem on the existence of the met-ric with given Ricci form is proved. Kähler-Einstein metrics with positive scalar curvatureon a compact manifold with positive first Chernclass are also discussed, and necessary and suffi-cient conditions for the existence of such a met-ric are presented. Examples of Kähler-Einsteinmetrics, especially on Fermat hypersurfaces aregiven, and there is an example of a manifoldwithout Kähler-Einstein metric. The mono-graph is well written and can be recommendedto anybody interested in the topic. (jbu)

V. A. Vassiliev, Introduction to Topology,Student Mathematical Library 14, AmericanMathematical Society, Providence, 2001, 149 pp.,US$25, ISBN 0-8218-2162-8The word Topology in the title of this bookmeans, roughly speaking, Algebraic Topology:homotopy, homology, cohomology, Morse theo-ry, Poincaré duality, degree of maps, and mani-

folds. The book explains what algebraic topolo-gy is, without assuming a deep knowledge ofgeneral topology. Because of this, many proofsare omitted or sketched. This is also due to awish to include a lot of material in 140 smallpages. Thus, the book will be very convenientfor those who want to be acquainted with thetopic in a short time, without going into manydetails (it works even better, if the book is com-plementary to lectures, as it was with theauthors lectures). Included in the text are a suf-ficient number of results, exercises and prob-lems. (mih)

D. Williams, Weighing the Odds. A Course inProbability and Statistics, Cambridge UniversityPress, Cambridge, 2001, 547 pp., £24.95, ISBN 0-521-00618-X, ISBN 0-521-80356-XIn the Preface the author warns that the bookhas many unusual features: this is why the bookis so interesting. In the parts devoted to proba-bility theory the results are precisely stated, butmost of the proofs are omitted. The sections onstatistics are nearly free from statements of tech-nical conditions under which the theorems hold.The book describes mainly the motivation ofprobabilistic and statistical thinking. One of thesections is called Sharpening our intuition: itseems that this would be a better candidate forthe title of the whole book. The authors viewsare declared very sharply and very clearly and,maybe, some readers will not agree with themcompletely; for example, the sentence on p. 223A celebrated result, the Neyman-Pearson lemma (notdiscussed in this book), does prove that the LR Test isunquestionally best (most powerful) in a certain sim-ple situation of little practical importance will beconsidered by many teachers as heretical butpractical statisticians may hold the same opinionas the author.

Although the author asserts that the bookcovers a very limited area, many topics are dis-

cussed here, both classical and modern. Theprobabilistic parts contain, for example, the lawsof large numbers, central limit theorems, thestrong Markov principle, generating functions,martingales, etc. Among the statistical topics wefind confidence intervals, Bayesian statistics, lin-ear models and ANOVA. The author charac-terises statistics as follows (see p. 381): I do apol-ogize that I often tell you that something is a good ideaonly to have to say later that it does not work in manyimportant cases. That is the way that Statistics is: fullof surprises and never dull . The last chapter isdevoted to quantum probability theory andquantum computing, which will probably be newto most readers.

The book is a rich and enjoyable source ofideas, motivations and examples, which can beused by teachers of probability and statistics. (ja)

R. J. Wilson, Stamping Through Mathematics,Springer, 2001, 126 pp., £17.00,11, ISBN 0-387-98949-8This book is really exceptional: there are only afew books of this sort. Despite the fact that itcontains a minimum of mathematics, it will beappreciated by many mathematicians, in partic-ular by those interested in stamp collecting. Thebook shows nice pictures of 400 stamps withoutdescriptions which are appreciated only by realcollectors. The book contains chapters of vari-ous kind. Here are some examples: the MiddleAges (Pope Sylvester II, Albertus Magnus andNicolas of Cusa), Globes, Nicolaus Copernicus(stamps of Poland, GDR and Venezuela), IsaacNewton (stamps of GB, North Korea, Monacoand Nicaragua), France and the Enlightment(dAlembert, Condorcet, Lagrange andLaplace), Russia (Kovalevskaya, Lyapunov,Ostrogradsky and Tchebychev), and much elsebesides. The book would be a nice present foranybody with interests in mathematics andstamp collecting as well. (jive)

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