1

BROCHURE DIDATTICA

CLASSE DI SCIENZE NATURALI

A.A. 2014-2015

2

Calculus

Teacher: Paolo Guiotto, UniPD – paolo.guiotto@unipd.it Motivations The course offers an introduction to the main ideas and tools of mathematical analysis motivating them by mathematical modelling of natural phenomena or applicative problems from physics, mechanics, probability, biology, finance, etc. Targeted audience First year students of science (with exception of students of mathematics, physics and engineering) or medicine. Syllabus. First part: Discrete Analysis

1. Discrete Evolution models (Malthus, Verhulst, logistic, Fibonacci). Concept of sequence and limit of a sequence. Main properties of limits. Concept of bigger order and asymptotic. Composed interest rates: the Neper number. Monotone sequences.

2. Infinite sums: concept of numerical series. Geometric and arithmetic series. Tests for convergence (ratio, root, comparison, Leibniz). Power series and applications.

Second part: Continuum Analysis

1. Continuum Evolution models. The concept of differential. Calculus with infinitesimals. Differentials of elementary functions. Rules of calculus. Fermat theorem: stationary points. Applications: the Snell law and the brachistochrone equation. Leibniz formula and optimization problems.

2. Primitives: methods of calculus. 3. Differential equations: first and second order linear, separable variables equations. Solution of the

brachistochrone equation. Pursuit curves. Teacher CV I'm researcher of mathematical analysis at University of Padova since 1998. I taught courses of mathematical analysis and probability for degree students of mathematics, physics and engineering and for PhD students in pure and applied math. My collaboration with the Scuola Galileiana starts in 2005. Along these years I've been tutor for several years, teacher of courses of mathematical analysis and probability. I taught the course of Calculus for the last two years. My scientific interests are in the field of analysis on infinite dimensional spaces with particular attention to measures on infinite dimensional space and stochastic partial differential equations. Textbooks/bibliography Lecture notes will be available.

3

Complements of analysis

Teacher: Carlo Mariconda - UniPD - carlo.mariconda@unipd.it Motivations. This course takes place in the first trimester of the first year, so it requires no specific mathematical backgrounds. One of the aims of the course is to give insights in some of interesting fields of mathematical analysis (still with plenty of open problems) by means of elementary tools. The topics of the course will be suited in real time depending on what the students are studying in their lessons at the university. Targeted audience. First year students in Sciences or Engineering. Syllabus. Part I. Finite sums: precise and approximate calculus. Discrete calculus: how to compute finite sums. The fundamental theorem of discrete calculus, the discrete Taylor expansion. Combinatorics revisited: the inclusion/exclusion principle; Stirling numbers of II type; an application to the calculus of finite sums of the powers of integers. The Euler-Maclaurin formula. Applications to sums of powers of integers (Bernoulli numbers), the approximation of the integral of a positive function (trapezoid rule), Stirling formula for the factorial. Part II. Discrete dynamical systems. Fixed points of a continuous map, attractive/repulsive points. Limits of orbits of systems induced by monotonic functions. Periodic points. Sarkovskii’s theorem. Cantor sets. Chaotic dynamical systems. Topological conjugacy. Teacher CV. Born in Reggio Emilia on October 8, 1964. 1976/82: French schools in Paris, Copenhagen, Milan. French Baccalauréat C. 1982/1987: University Studies at Padova, degree in Mathematics. Thesis with Prof. Arrigo Cellina “The Kuratowski index of a decomposable set”. 1987/1991: Ph.D. student at SISSA/ISAS of Trieste. Ph.D. thesis with Prof. Cellina on the calculus of variations 1992 and 1995: research activity in Paris with Raphael Cerf at the Ecole Normale Superieure and Paris VI 1992: Ricercatore at the University of Padova, Faculty of Sciences 1998: Associate Professor at the University of Padova, Faculty of Engineering 1998-2014: participation and leader of various research groups. Courses in Calculus, Mathematical methods for engineers, Discrete Mathematics and probability. Ph. D. courses in Padova and Evora (Portugal). Research interests: Functional Analysis, Calculus of variations. Collaborations: A. Cellina, M, Amar, R. Cerf, G. Treu, S. Solimini, G. De Marco, P. Bousquet. Textbooks/bibliography C. Mariconda & A. Tonolo, Calcolo Discreto: metodi per contare, Apogeo R. Devaney, An introduction to chaotic dynamical systems, Addison-Wesley.19

4

Introduction to probability models

Teacher: Alessandra Bianchi, UniPD - alessandra.bianchi@unipd.it Motivations. The aim of the course is to provide an introduction to elementary probability theory and its application to sciences. The typical environment will be that of discrete probability spaces that will be introduced in the first lectures together with some basic probability tools. By the construction and the analysis of suitable models, it will be then shown how probability can be applied to the study of phenomena in physics, computer science, engineering and social sciences. In turns, this will led to the discussion of some open problems of the field.

Targeted audience. The course will be self-consistent and no specific mathematical knowledge is required. Logic and a scientific attitude are always helpful.

Syllabus. - First elements of probability theory: Discrete probability spaces; Combinatorics; Conditional

probability; - The Ising model in statistical mechanics: Definition and properties; Analysis of phase transitions in

dimension 1 and 2; - Discrete random variables: Discrete distributions, mean value, independence; Binomial and

geometric distribution; Moments generating function; - Applications to two common problems: The coupon collector problem; Shuffling a deck of cards; - The symmetric random walk in one and higher dimensions: Definition and properties; Reflection

principle and return probability at 0; Analysis of transience and recurrence; - Electrical networks and random walk on graph: Elements of discrete potential theory; Harmonic

functions and their probabilistic interpretation; Random walk on general graphs; - Application to the gambler’s ruin problem: probability of loss and win in a gambling game; - Markov chains (theory): Definition and classification of Markov chains in finite space; Stationary

distribution and ergodic theorem; - Markov chains (examples and applications): Eherenfest model; Bernoulli- Laplace model; Galton-

Watson branching process; - Elements of Monte Carlo method: Definition of Monte Carlo Markov Chain (MCMC); examples and

application to optimization problems. Teacher CV. Born on 31/12/1977 Education and positions

- July 2003 degree in Mathematics - University of Bologna - April 2007 PhD degree in Mathematics - University of Roma Tre - 2007-2009 postdoc fellow at the WIAS of Berlin (Germany) - 2010- 2012 postdoc fellow at the Mathematics Dep. of Bologna - Since May 2012 Assistant Professor ("Ricercatore") of Probability and Statistics at the

Mathematics Dep. of Padova. Research interests: probability and Statistical Mechanics, Metastability in Markovian processes, Stochastic dynamics and relaxation time, Interacting particle systems on random structures She published 8 articles on international journals and gave around 30 talks to students and experts of the field. Teaching: 2010&2011&2012: Probability and statistics – University of Bologna; 2012&2013&2014: Statistics – University of Padova; 2014: Introduction to Probability models- Galilean School of Padova. Since 2012, responsible of the FIRB project "Stochastic Processes and Interacting Particle Systems". Textbooks/bibliography 1. F. Caravenna, P. Dai Pra. Probabilità. Un primo corso attraverso modelli e applicazioni, Springer (2013). 2. W. Feller. An Introduction to Probability Theory and its Applications. I Volume, Third edition, Wiley (1968). For consultation: 3. P. G. Doyle, J.L. Snell. Random walks and electric networks. Carus Mathematical Monographs, 22, Mathematical Association of America (1984). Available online. 4. D. A. Levin, Y. Peres, E. L. Wilmer, Markov Chains and Mixing Times, American Mathematical Society, Providence, RI (2009). Available online. 5. O. Haggstrom. Finite Markov Chains and Algorithmic Applications. Cambridge University Press (2002). Available online.

5

Introduction to thermodynamics

Teachers: Fulvio Baldovin and Enzo Orlandini - UniPD fulvio.baldovin@unipd.it, enzo.orlandini@unipd.it

Motivations Thermodynamics is a basic interdisciplinary subject which bridges over different areas of Science, including Physics, Mathematics, Chemistry, Engineering, Biology, and Medicine. Although common to many Bachelor curricula, time constraints and needs of focusing on practical application in the specific field tend to hinder the presentation of the simple, symmetric structure which underlies Thermodynamics. As a consequence, Students may be confused about the meaning and use of different thermodynamic potentials and response functions. Goal of the present course is to introduce the thermodynamics of simple systems. While keeping mathematical aspects at a level suitable for first-year undergraduate students, emphasis will be given to the equivalence of the Entropy and Energy representations, which through Legendre transformations generate all other potentials. Exemplifications and case of study from different fields will help the application and the comprehension of the formal structure.

Targeted audience The course targets the Natural Science Class of the Galileian School of the University of Padova, including students in Physics, Mathematics, Chemistry, Engineering, Biology, and Medicine. The ideal audience is supposed having been exposed to an introductory course of Mathematical Analysis in one variable, while a practical knowledge of partial derivatives and Legendre transformations will be offered within the course's lectures.

Syllabus• Macroscopic measurements • Composition of thermodynamic systems • Measurability of energy and heat • Thermodynamic walls and constraints • Thermodynamic equilibrium • The fundamental problem of

Thermodynamics • Entropy and Energy representations • The postulates of Thermodynamics • Intensive parameters and equations of

state • Thermal, mechanical and chemical

equilibrium • The Euler equation • The Gibbs-Duhem relation • The simple ideal gas • The ideal van der Waals fluid

• Electromagnetic radiation • Possible, impossible, quasi-static, and

reversible processes • The maximum work theorem • Engine, refrigerator, and heat pump

performance • The Carnot cycle • Power output and endoreversible engines • Legendre transformations • Thermodynamic potentials • The Gibbs potential and chemical

reactions • Response functions and Maxwell relations • Stability of thermodynamic systems • Le Chatelier's principle and Le Chatelier-

Braun principle • Role of symmetries in Thermodynamics

Teacher CV Fulvio Baldovin is Assistant Professor in Physics at the Physics and Astronomy Department of the University of Padova. He is author of about 40 original research articles in international journals. He teaches Statistical Mechanics for the Ph.D. degree in Physics, and Biological Physics for the Bachelor degree in Molecular Biology. He is tutor in Theoretical Physics for the Galileian School of the University of Padova. He actively collaborates with Complex Systems groups at the Weizmann Institute in Israel, and Ecole Central Paris. Enzo Orlandini is Associate Professor in Physics at the Physics and Astronomy Department of the University of Padova. He is author of about 150 original research articles in international journals. He teaches Statistical Mechanics for the Master and Ph.D. degrees in Physics, and General Physics for the Bachelor degree in Molecular Biology. He actively collaborates with Soft Matter groups at the Edinburgh University, Oxford University, and SISSA in Trieste. Textbooks/bibliography H.B. Callen, Thermodynamics and an introduction to Thermostatistics – Second Edition, Wiley. A number of problems and examples will be explicitly solved at the blackboard.

6

Measure theory

Teachers: Paolo Ciatti and Pier Domenico Lamberti - UniPD paolo.ciatti@unipd.it, pierdomenico.lamberti@unipd.it Motivations. This lecture course is an introduction to a number of modern techniques in real analysis with focus on measure theory and the theory of integration. The material will be presented in an abstract setting including as a special case the Lebesgue theory of integration in the n-dimensional Euclidean space. This case will be discussed in detail and will serve as a source of examples and motivations. The Lebesgue integral is a standard tool in contemporary scientific literature and it is a matter of folklore to say that it is a flexible integral allowing the proof of powerful theorems such as the celebrated Dominated convergence Theorem. In fact, the main reason for its success is much deeper and is related to the completeness of the corresponding L

p-spaces, a fact of fundamental importance in mathematical analysis

and its applications. For example, the completeness of such spaces allows to prove the existence of minimizers in important problems in the calculus of variations. Targeted audience. This lecture course is particularly directed to students in Mathematics, Physics and Engineering. However, students from other scientific disciplines may take advantage of a rigorous presentation of fundamental notions from measure theory which are often assumed to be known without providing a proof. A basic course in calculus would cover all necessary prerequisites. Syllabus. Part a: σ-algebras and measures; Measurable sets and Caratheodory's Theorem; Borel measures on the real line. Remarkable examples: Cantor-type sets, Vitali set, a Lebesgue measurable set which is not a Borel set. Measurable functions and definition of integrals for real or complex-valued functions defined on a general measure space. Main theorems for taking the limit under the integral sign: Monotone convergence Theorem, Fatou's Lemma, Dominated convergence Theorem and integration of series. Part b: Lebesgue measure in the n-dimensional Euclidean space and Fubini-Tonelli Theorem. Riesz-Fischer Theorem and completeness of the spaces of integrable functions. The spaces of square integrable functions and basic theory of Hilbert spaces. Differentiation of the Lebesgue integral and the Hardy-Littlewood maximal function. Applications to ergodic theory. Teacher CV. Paolo Ciatti. Undergraduate Education: Laurea in Fisica, Università di Torino,1990. Thesis directed by Prof. Tullio Regge. Graduate Education: PhD in Mathematics, Politecnico di Torino,1995. Thesis directed by Prof. Fulvio Ricci. Academic Positions: Junior Researcher, University of New South Wales (Sydney),1996-1997. Ricercatore, Università di Padova, 1998-2008. Professore Associato, Università di Padova, 2008-present. Adjoint Professor, Dalhousie University (Halifax, Nova Scotia), 2013-present. Pier Domenico Lamberti is Researcher in Mathematical Analysis at the Department of Mathematics of the University of Padova since 2006. He got his PhD in Mathematics from the University of Padova in 2003. His scientific interests are mainly in spectral perturbation problems for partial differential operators of elliptic type and include real and functional analysis, theory of function spaces, linear and non-linear spectral theory and calculus of variations. He has also been interested in didactics of mathematical analysis. He is the author of more than thirty publications in international journals, some of which have been jointly written with his students. He has been visiting a number of mathematical institutions in several countries and he has participated into many international conferences. He has been supervising several undergraduate students and he is currently supervising two postgraduate students. Textbooks/bibliography Folland, Gerald B. Real analysis. Modern techniques and their applications. 2nd ed. Pure and Applied Mathematics. A Wiley-Interscience Series of Texts, Monographs, and Tracts. New York, NY: Wiley. (1999).

7

Interaction networks in living systems Teacher: Amos Maritan - UniPD - amos.maritan@unipd.it Motivations The understanding of living systems, which span 21 orders of magnitude in mass, needs more than a mere generalization of our knowledge of inanimate matter. However the use of the paradigm of interaction networks has allowed to tackle, in a unified framework, complex interdisciplinary problems in biology, ecology and social systems. Such problems exhibit recurrent and universal patterns reminiscent of certain thermodynamic systems poised near a critical point. The three main aims of the course are: 1) to stimulate a scientific attitude when facing a wide variety of natural phenomena without prejudice; 2) to be able to identify some of the key characteristics responsible for the emergence of a phenomenon; 3) to provide general tools, both analytical and numerical which are fundamental for the development of appropriate models for the phenomenon to be understood.

Targeted audience The program of the course has some flexibility and may depend, to some extent, on the preparation/ interests of students. This course can be held in the second or later year. It will be of interest for all students of the Galilean School. In the case all students attending the course are from natural science and engineering some sophisticated math will be utilized, otherwise the two courses of “Calculus” and “Probability” in the first year of the GS will be sufficient.

Syllabus Introduction: aims of the course; overview of various examples. Network theory: deterministic and random networks; random walk on networks; electrical networks; Erdos-Renyi networks; degree distribution; Barabasi Albert model; Small Worlds. Scaling theory: Probability distribution function with and without a characteristic scale; playing with power laws; fat tailed distributions. Examples of power law distributions: body mass – metabolism scaling; power laws in cities; power laws in written human communication; spontaneous brain activity etc. Species interaction networks: Dynamical stability of large and complex interacting systems (with a brief introduction to the random matrix theory); complexity-stability paradox; mutualistic and antagonistic networks; emergence of nested interaction networks in mutualistic systems. Food trade networks: analysis of existing data and emerging patterns; dynamics of the food trade and its stability. Optimization principles in Nature: Examples of variational principles in physics; Natural selection and optimization; examples of optimization in interaction and transportation networks. Each “chapter” will have homework where each student is encouraged to find him/her-self examples and data where to apply the theory and the data analysis he/she has learnt.

Teacher CV Professional experience: Prof. of Physics, Padova (2003 - ), Prof. of Physics, SISSA Trieste – Italy (1994 -2003 ); Associate Prof. of Physics, Padova (1991 - 1994 ); Associate Prof. of Physics , Bari (1987 - 2001); Associate Prof. of Physics, Padova (1983 - 1987). Education and training: Physics degree at Padova (1979); Ph.D. in Physics at SISSA, Trieste (1983). Accademic Appointments: Dean of the School of Excellence “Scuola Galileiana di Studi Superiori”, (2004 - 2010). Scientific consultant, ICTP Trieste – Italy (1997-2003). Correspondent resident member of "Istituto Veneto di Lettere Scienze ed Arti (2006-). Thesis: About 30 PhD students, 40 undergraduate students. Summary: the main field of interest is the equilibrium and non-equilibrium statistical mechanics. The main focus is on problems at the interface between physics and biology. 300 publications in refereed journals including 4 in Science, 12 in Nature, 21 in Proc. Nat. Acad. (USA), and 64 in Phys. Rev. Lett.; 1 book co-edited; 1 patent. More at http://www.pd.infn.it/~maritan/index.html

Textbooks/bibliography

1. M.E.J. Newman, Network: an introduction, Oxford University press (2010). Only few chapters. 2. M.E.J. Newman, Power laws, Pareto distributions and Zipf's law, Contemporary Physics, Vol. 46, No. 5,

September–October 2005, 323 – 351. 3. R. M. May, Stability and complexity in model ecosystems, Princeton Uniuversity press (2001). 4. Chapters 1-3 and 7 and some parts of the remaining chapters.

Various articles will be proposed for each “chapter” of the course. The suggested articles will be chosen depending on the student interest and preparation.

8

Open problems in the physics of fundamental interactions

Teacher: Massimo Pietroni – INFN - pietroni@pd.infn.it Motivations. The Standard Model provides a complete and successful description of all the particle physics experiments conducted so far, from low energies to the Large Hadron Collider. At the same time, a Cosmological Standard Model has been shaped by a wealth of observations culminating in the Cosmic Microwave Background measurements by the Planck satellite and in the observation of primordial gravitational waves by the Bicep2 telescope. These undisputable successes open the way for a more profound investigation on the nature of the fundamental interactions governing the phenomena of particle physics and cosmology. The course is designed to provide a general overview of the main open problems in these fields, from the need to extend the Standard Model of particle physics, to the nature of cosmological dark matter and dark energy. Emphasis will be put on the conceptual rather than on the technical aspects, with the aim of highlighting the present status of the field, the most active areas of investigation, and the landscape of existing ideas to solve the open problems. Targeted audience. The style of the presentation will be calibrated to a second-year student in the Class of Natural Sciences, not necessarily in Physics. Syllabus.

- Symmetries and Symmetry Breaking (use of symmetries in the solution of physical problems; discrete and continuous symmetries in particle physics; Standard Model; Grand Unification beyond the Standard Model);

- The masses of elementary particles (Higgs mechanism; hadron masses; neutrino masses); - The hierarchy of physical scales: physical theories as effective theories; - Cosmology and its impact on the physics of fundamental interactions (Inflation; Dark Matter; Dark

Energy; the cosmological asymmetry between matter and antimatter). Teacher CV. Massimo Pietroni, born in Trieste, 31/5/1966. Academic degrees: Laurea in Fisica, University of Trieste, 1990; PhD in Physics, University of Padova, 1994. Postdoctoral positions: DESY-Hamburg, 1993-1995; CERN, Geneva, 1995-1997. Current affiliation: Department of Physics, Parma University (on detachment from INFN). Permanent positions: INFN Padova - Ricercatore 1998-2007; Primo Ricercatore 2008-… University teaching: 2013-2014: “Fundamental Interactions”, 40 hours, Department of Physics, Parma University; 2006-2012: Cosmology Course for PhD students, 20 hours, Physics Department, Padua University; supervisor of 6 PhD students and 7 undergraduates. Teaching at International Schools: December 2011: LACES 2011, Galileo Galilei Institute, Florence, Italy. "Cosmology” (8 hours); April 2011: XXVI Heidelberg Physics Graduate Days, Heidelberg, Germany: "Cosmological Perturbations for the large scale structure of the universe” (15 hours); February 2008: Schladming Winter School "Non-equilibrium aspects of Quantum Field Theory From cosmology to table-top experiments", Schladming, Austria (8 hours). Textbooks/bibliography: - Gian Francesco Giudice, “A Zeptospace Odissey: A Journey into the Physics of the LHC”, Oxford U. P., 2009; - Gianfranco Bertone, “Behind the Scenes of the Universe - from the Higgs to Dark Matter”, Oxford U. P., 2013; - notes by the teacher.

9

Chemical equilibrium and irreversible processes Teacher: Giorgio Moro - UniPD - giorgio.moro@unipd.it Motivations In many fields of science, engineering and medicine the study of complex material systems and their time evolution is required on the basis of macroscopically measurable properties. The classical thermodynamics and its extension to irreversible phenomena provide the essential tools for treating these this kind of problems within an unified framework. The main topics of the course, i) the equilibrium in complex chemical systems and ii) the basic description of irreversible processes starting from chemical kinetics, allow a focus on issues of general interest in several branches of science and technology, which are shared by different educational curricula at the University. Targeted audience Second year students of science, engineering and medical curricula, that have already acquired the basic knowledge on the principles of thermodynamics and their applications to simple material systems Syllabus. Résumé of Thermodynamics principles and use of thermodynamical state functions. Equilibrium in the presence of chemical reactions and of phase transfer. Tables of thermodynamical standard properties and predictions of equilibrium states. Macroscopic description of chemical kinetics and molecular models of reaction mechanisms. Catalysis and kinetic models of the effects of enzymes. Fluxes and Entropy production in the Thermodynamics of irreversible processes. Thermal diffusion, viscous flow and mass transport by diffusion. Teacher CV Giorgio Moro has got the University degree in Chemistry in 1975 and, after two years of post-doc at Cornell University (Ithaca, N.Y., USA), has been research assistant and associate professor at Padua University and Parma University. Presently he is full professor of Physical Chemistry at the Department of Chemical Sciences of Padua University. His main research interests concern Theoretical Chemistry with applications to the study of molecular dynamics in condensed phases, like: interpretation of dynamical effects in Magnetic Resonance, conformational dynamics, molecular models of activated processes, structural and transport properties of liquid crystals, statistical properties of quantum pure states. Textbooks/bibliography P. Atkins, J. de Paula, “Chimica Fisica” (4

a Ed., Zanichelli , Bologna, 2010)

H.B. Callen, “Thermodynamics and an Introduction to Thermostatics” (2nd

Ed., Wiley, New York, 1985) I. Prigogine, “Introduzione alla Termodinamica dei Processi Irreversibili” (Leonardo, 1971, Roma)

10

Measurement instruments and techniques

Teacher: Giovanni Carugno - INFN - carugno@pd.infn.it Motivations Science require instruments to probe the nature of the processes. The physical basis of the main instruments and techniques will be presented. The Course will cover four different subjects: a) Vacuum, b) Cryogenic, c) Electromagnetic Sources and Detectors and d) Signal treatments and Noise Sources. These areas have grown through the years so to open the access to the discovery of new phenomena. Through these series of lectures we will examine the ideas and implementation behind most of the technique we are presently using in most of our laboratory and also in everyday life. Targeted audience. The Course will be mainly targeted in principle to all students of the Natural Sciences branch of the SGSS, as it will cover different aspects of present technologies and instruments that found a large diffusion in many laboratory activities. For instance, the photonic handling of sources and detectors is covering most of the disciplines with the help of pulsed laser in the femtosecond region. Syllabus. Vacuum: Kinetic theory of gas, Vacuum Pumps from low to UHV systems, Gauge Instruments and Residual Gas Analysis. Cryogenic: Heat Capacity,Thermal Conductivity, Thermal Expansion at Low Temperature. Liquid Cryogenic Production through the Joule Thompson Expansion. Storage Vessel: Dewar. Adiabatic Magnetization Refrigeration for Electron and Nuclei: from millikevin to microkelvin. Electromagnetic Source and Detectors: Radio Wave Antenna Emission Pattern and Power. Satellite and Radar vs Microwave Apparatus. Optical Source: from Incoherent to Coherent (Lamp & Laser) X-rays Synchrotron Machine. E.M. Detectors: from Electric Field to Energy Photons measurements. Signals Treatment and Noise Sources: Signal/Noise requirements; few examples. Signal Extraction: Averaging, Box integration, Lock-in technique, Filtering. Johnson Noise, Shot Noise, 1/f Noise and extrinsic noise sources. Teacher CV Laurea Degree (May 1986) Physics, University of Roma “La Sapienza” (laurea Summa cum laude). Supervisor: Prof. M. Conversi. Student Associate at Cern and Brookhaven National Laboratory (1985 - 1986). CERN fellow (1987 – 1988) ; Supervisors: Prof. C. Rubbia, M. Ferro-Luzzi. Associate Scientist at Legnaro National Laboratory (1989 – 1992). Researcher at INFN Sezione di Padova (1993 – 2002 ). Visiting Scientist at Paul Scherrer Institute (PSI – Zurich) (1993 – 1994 ). Visiting Scientist at CERN and ESPC Paris under European Contract provided by Prof. G. Charpak (1996). 1° Ricercatore at INFN Padova (2002 – 2013). Research Grant from Schwinger Foundation (2008). Distinguished Member of European Casimir Network ESF (2008 – 2013 ). Textbooks/bibliography : 1) Melissinos: Introduction to Modern Technology, Cambridge University; 2) Varian: Corso sul Vuoto; 3) European Course on Cryogenic; 4) J.Moore et al.: Building Scientific Instruments , Addison Wesley; 5) E.R.Davies: Electronic Noise and Signal Recovery, Academic Press; 6) D.Preston E.Dietz: The art of Experimental Physics, John Wiley.

11

Probability and introduction to stochastic processes

Teacher: Paolo Dai Pra - UniPD - paolo.daipra@unipd.it Motivations The purpose of the course is to present some fundamental stochastic models with a spatial and/or temporal structure. This will serve as motivation for the introduction of some basic notions concerning stochastic processes and random fields, although the emphasis will be on applications. Targeted audience Students enrolled in a degree in natural or social sciences. Basic knowledge of calculus and elementary probability will be assumed. Syllabus The program could in principle be calibrated to the audience. A possible program is the following. 1. Stochastic independence. 0-1 laws. Applications to percolation models. 2. Random walks. Applications to random polymer models. 3. Brownian motion: construction and properties of the sample paths. The invariance principle. Points 1. and 2. above could be replaced by models related to life and social sciences, such as models for population or opinion dynamics. In this case some notions on continuous-time Markov chains will be introduced. Teacher CV. Paolo Dai Pra is Full Professor in Probability and Mathematical Statistics at the Department of Mathematics of the University of Padova. Besides the teaching activity at the undergraduate level, he has delivered several courses for the Doctoral School in Mathematical Sciences and the Galilean School. His research interests are mainly concerned with stochastic models for systems of many interacting components, their thermodynamic limit, phase transitions, fluctuations, large deviations and convergence to equilibrium. More details are available at: www.math.unipd.it/~daipra Textbooks/bibliography Lecture notes will be prepared. For the program exemplified above, notes will be based on the following texbooks: A. Klenke, Probability Theory, Springer, 2008. G. Giacomin, Random Polymer Models, Imperial College Press, 2007. I. Karatzas and S.E. Shreve, Brownian Motion and Stochastic Calculus, Springer, 1998.

12

Foundations of differential geometry

Teachers: Franco Cardin and Andrea Giacobbe – UniPD franco.cardin@unipd.it, andrea.giacobbe.1@math.unipd.it Motivations Part-1 (AG): the concepts of manifold and charts will be introduced. Then, starting from vector fields and differential forms, we will discuss tensor calculus and operations with tensors. We will finally introduce orientability and integration on manifolds. In part-2 (FC) some elements on symplectic Hamiltonian geometry and dynamics will be introduced, in order to analyze in some detail the standard concepts of the Calculus of Variations and to discuss around the quality of the critical curves, by means of the conjugate points and the Morse index theory. Targeted audience Students in Mathematics, Physics, Engineering, or other science degree course. Syllabus Manifolds, atlases, tangent and cotangent bundle; vector fields, differential forms, properties of such objects. Tensors and tensorial calculus; integration on manifolds (Stokes theorem). An elementary introduction to symplectic manifolds. Hamiltonian dynamics in this new environment. Lagrangian submanifolds. A new geometric look on the solutions of Hamilton-Jacobi equations. A refresh on the standard Calculus of Variations, the Action functional. Conjugate points theory. Morse index theory, in the more simple cases. A discussion about applications to geodesic motions and phase transitions. Teacher CV Franco Cardin. Laurea in Physics, Univ. of Padova. He has been CNR researcher, universitary researcher, associate professor, since 2000 he is full professor in mathematical physics, MAT07, at the Department of Mathematics of the University of Padova. Scientific interests: continuum thermo-mechanics and phase transitions; the global theory of Hamilton-Jacobi and allied variational theories of symplectic topology; topics on exact finite reduction in field theory. Recent international research collaborations: in symplectic topology, with the Ecole Polythecnique; in molecular dynamics, with the Computational Laboratory of Zurich. F.C. spent periods of study and research at the Foettinger Institut of the TU of Berlin, guest of Prof. Ingo Mueller; at the university Paris VI, guest of Prof. Charles Marle, at the Ecole Polythecnique, guest of Prof. Claude Viterbo, director of the Centre de Mathematiques Laurent Schwartz. He is member of the Scientific College and Coordinator of Course of Studies in "Mathematics" of the "Scuola di Dottorato in Matematica" of Padova. Andrea Giacobbe. Bachelor in Mathematics (Padova) PhD in Mathematics (Padova and Univ. of Maryland), post doc in Padova (2000-2002) and Utrecht (2002-2004) he is researcher in mathematical physics since 2005 at the the University of Padova. Scientific interests: dynamical systems, in particular completely integrable Hamiltonian systems and systems with symmetries, and in fluid-dynamics, in particular spectral and Lyapunov stability. He has international collaborations with B. Zhilinskii and D. Sadovskii (Univ du Littoral), Mardesich (Dijon), Efstathiou (Groningen), Fasssò (Padova), Mulone (Catania). Textbooks/bibliography: J.Milnor: Morse Theory, Princeton University Press (1963). B.A.Dubrovin, A.T.Fomenko, S.P.Novikov: Modern Geometry, methods and appls, Springer (1988) F.Cardin: Elementary Symplectic Topology & Mechanics, draft (2014) Spivak, Calculus on Manifolds, Addison-Wesley (1965). Bott & Tu, Differential Forms in Algebraic Topology, Springer GTM 82 (1982).

13

General relativity

Teacher: Kurt Lechner – UniPD – kurt.lechner@unipd.it

Motivations. The course is aimed to furnish the mathematical and physical foundations of the theory of General Relativity - the theory describing Gravity in compatibility with Einstein’s relativity principle. The theory is constructed considering as basic physical cornerstone the equivalence principle and translating it in the mathematical paradigm of General Covariance. Differential Geometry must arise as a compelling consequence of physical observations, not as a ``dogma’’ of mathematical prejudices. After the so constructed theory comparison between predictions of General Relativity and ``classical’’ as well as recent experiments will play a basic role in the second part of the course. Connections between mathematical solutions and more speculative phenomena such as black holes, acceleration of the universe and gravitational waves will also be made.

Targeted audience. The course is targeted for students possessing basic knowledges of Classical Electrodynamics, especially Maxwell equations and their main solutions and Special Relativity formulated in the framework of the the covariant tensor formalism.

Syllabus. Introduction. Foundations of special relativity. Gravity against the other fundamental interactions. The postulates of special relativity and the tensor calculus. A relativistic theory of Gravitation. Equivalence principle. Metric tensor, connection and geodesics. Newtonian limit and gravitational red-shift. The principle of General Covariance. Elements of Differential Geometry. Differentiable manifolds and diffeomorphisms. Tensors. Pseudo-Riemannian manifolds. Affine connection and covariant differentiation. Curvature and Riemann tensor. Physical systems in external gravitational field. The minimal coupling to gravity. Electrodynamics in an external gravitational field. Conservation of electric charge and four- momentum. Einstein’s equations. Derivation of Einstein’s equations. Cosmological constant. The energy- momentum tensor of the gravitational field. Postulates of General Relativity: local and global causality. Schwarzschild solution. Spherical solution of Einstein’s equations. Classical experimental tests of General Relativity. Black holes. Global analysis of geodesics in the Schwarzschild metric. Qualitative analysis of geodesics. Event horizon and Kruskal metric. Hawking radiation. Gravitational waves. Solutions of Einstein’s equations in the weak field limit. Plane waves. Energy lost by oscillating masses. The decay of the period of the binary pulsar PSR 1913+16 as evidence of the existence of gravitational waves. Brief introduction to the cosmological standard model. Basic elements. Formal developments. The least action principle in General Relativity. The Einstein-Hilbert action for the gravitational field.

Teacher CV. Born: 15/05/1962 (Brixen, Italy) Education: Laurea in Physics, University of Padua (1986, November). Magister Philosophiae, International School for Advanced Studies, Trieste, (1989, October). - Doctor Philosophiae, International School for Advanced Studies, Trieste, (1990, April). Academic positions and duties: Researcher for Theoretical Physics, Dept. of Physics, Univ. of Padua (1990-2004). Associate Professor for Theoretical Physics, Dept. of Physics and Astronomy, Univ. Of Padua (since 2004). Member of the Dept.’s council (2003). Member of the Teaching Committee of the Dept. of. Physics (since 2004) Member of commettees for permanent research positions in Theoretical Physics at the Universities of Milano (2000), and Cagliari (2002). Teaching and tutor activities: Courses on ``General Physics I and II’’, ``Relativity’’, ``Thermodynamics’’, ‘’Electromagnetic fields’’, ``Theoretical Physics’’, ``Mathematical Methods for Physics’’ at the Faculties of Sciences and Engineering and the ``Scuola Galileiana di Studi Superiori’’. Tutor for the students of the the ``Scuola Galileiana di Studi Superiori’’ (2006-2011). Research fields: Superstring-theory and M-theory. Supergravity theories. Superstring loop amplitudes. Anyons and Chern-Simons theories. Quantum Anomaly cancellation. Spin-statistics connection, covariance and duality in field-, brane- and string-theory. Radiation reaction and selfinteraction for charges, dyons and branes. Author of about 50 publications on international journals. www.slac.stanford.edu/spires/find/hep/www?rawcmd=FIND+A+LECHNER. Book author: ``Elettrodinamica Classica’’, 570 pg., Springer-Verlag, Milano, 2014. Textbooks/bibliography 1) S. Weinberg, ``Gravitation and Cosmology’’, Wiley, New York, 1972. 2) S.W. Hawking and G.F.R. Ellis, ``The large scale structure of space-time’’, Cambridge University Press, London, 1973. 3) M. Gasperini, ``Relativita’ Generale e Teoria della Gravitazione’’, Springer-Verlag, Milano, 2010.

14

Life sciences 1 - mitochondrial medicine

Teacher: Massimo Zeviani – Cambridge, UK - mdz21@mrc-mbu.cam.ac.uk Motivations. Mitochondria are crucial for life in most eukaryotes. Mitochondrial biology is an extremely complex field, overarching a range of diverse issues, from the structural and mechanistic definition of the mitochondrial bioenergetics machinery, to the genetics and evolution of mtDNA, to the role of mitochondrial in cell signalling and homeostasis. Gene mutations related to mitochondria are responsible of a highly heterogeneous group of “primary” mitochondrial disorders, but dysfunction of mitochondrial bioenergetics is also involved in a number of human pathological conditions of high social relevance, from age related neurodegeneration to diabetes and the metabolic syndrome, ischemia-reperfusion damage, and even cancer and inflammation. This course will address the fundaments of mitochondrial biochemistry, genetics and evolution, to then address the etiology and pathomechanisms of mitochondrial dysfunction and their implications for human health. Targeted audience. Although the course will be mainly targeted to students in Biology, Biotechnology and Medicine, as it will cover different aspects of mitochondrial function in cells, tissues and whole organisms, students with different backgrounds will be welcome as well. Syllabus. Mitochondria as the powerhouse of the cell; mitochondrial as the driving force for eukaryotic evolution; the peculiar double genetics of mitochondrial control; the fundaments of mitochondrial medicine; mitochondrial in ageing, age-related disorders and metabolic derangement. Mitochondria are double membrane cytoplasmic organelles resulting from a primordial endosymbiotic event that gave rise to modern eukaryotes. Mitochondria are the major source of the high-energy phosphate molecule, adenosine triphosphate (ATP), which is synthesized by the mitochondrial respiratory chain (MRC) through the process of oxidative phosphorylation (OXPHOS). OXPHOS is a complex biochemical process, carried out through the dual control of physically separated, but functionally interrelated, genomes, nuclear and mitochondrial DNAs

1. Multiple copies of mtDNA are present in each

mitochondrion, whose maintenance and expression is carried out in situ through autochthonous pathways. In sexuate organisms, mtDNA is transmitted uniparentally through the female gamete. The genetic and biochemical intricacy of mitochondrial bioenergetics explains the extreme heterogeneity of mitochondrial disorders,, a group of highly invalidating human conditions, predominantly affecting the nervous system and skeletal muscle, and causing substantial morbidity and premature death

2. Although energy failure

associated with reduced ATP biosynthesis appears to be critical in individual or combined MRC-complex defects, other mechanisms are also likely to be involved, and are probably predominant in the pathogenesis of specific syndromes, such as alterations of cellular reduction-oxidation status, production of reactive oxygen species (ROS), compromised Ca

2+ homeostasis, and dysregulation of mitochondrial

dynamics, autophagy or apoptosis3.

Teacher CV. Massimo Zeviani graduated cum laude in Medicine at the University of Padua. He specialised in Endocrinology and Neurology, and obtained a PhD in Genetics at the University René Descartes in Paris. In 1984, he moved to Columbia University, New York, where he worked as a post-doc and research scientist for five years with Prof. Salvatore Di Mauro on the biochemical and molecular definition of respiratory chain disorders. In 1990, he became Assistant and then Associate in Neurology at the Department of Biochemistry and Genetics of the Istituto Neurologico "C. Besta" in Milan where he organized a laboratory of molecular biology on mitochondrial disorders. In 2001 he became the director of the Unit of Molecular Neurogenetics and, in 2011 he became the director of the Department of Molecular Medicine of the same Institute. In January, 2013, he was appointed Director of the MRC Mitochondrial Biology Unit in Cambridge, UK. Author of ≈300 scientific publications in peer-reviewed journals, he has identified and characterized numerous disease genes associated with OXPHOS defects, contributing to the elucidation of the molecular pathogenesis of mitochondrial disorders. More recently he focused on the development of therapeutic approaches to treat these conditions in experimental models and, eventually, patients. Textbooks/bibliography 1) Zeviani M and Di Donato S. Brain. 2004: 127:2153−72. 2) Elliott HR, et al. Am J Hum Genet. 2008; 83(2):254−60. 3) Wallace DC. Annu Rev Genet. 2005: 39:359−407. 4) Zeviani M, Carelli V. Mitochondrial disorders. Curr Opin Neurol. 2007;20:564-71. Review.

15

Life sciences 2 – GMOs in the genomics era

Name of the teacher: Gianni Barcaccia – UniPD – gianni.barcacca@unipd.it

Motivations. Spreading theoretical knowledge and actual potentials of advanced biotechnologies, with particular reference to genetically modified organisms (GMOs), in crop and livestock species in the era of genomics. The production and/or adoption of transgenic crop plants and animal breeds in agriculture systems is one of the main issues in public opinions and political debates because they raise several doubts and environmental concerns in relation to food safety and biodiversity safeguard. Furthermore, transgenic plants and animals are produced and exploited also for basic studies, like for instance those of genomics dealing with gene expression and function in laboratory model animals and plants. Basic and robust information is crucial for understanding what happens in this area of research and for discriminating what is good and true from what is bad and false or misleading. The advancement and acquisition of scientific knowledge in this subject is also important because the debate on GMOs and other biotechnologies is unfortunately affected by personal attitudes and believes that may lack of any scientific fundamentals since very often these subjects are faced superficially at the societal and political levels by uninformed persons.

Targeted audience. Motivated students who may be attracted, in general, by topics related to life sciences and, more specifically, interested to highly debated hot topics of modern genetics, focusing on genetically modified organisms (GMOs) and other biotechnologies (e.g. cloning and breeding) applied to crop plants and animal breeds, including model (laboratory) organisms. Targeted audience may also include students sharing concern for the environment and paying attention to livestock safety and plant germplasm diversity, and to the quality and salubrity of foodstuffs.

Syllabus. General introduction to the area of genetically modified organisms (GMOs) and other biotechnologies (e.g. cloning and DNA marker-assisted breeding). Definition of transgenic organisms. Answers to important questions: how and why are they produced? Main methods of genetic transformation in plant and animal species. Concepts of gain-of-function (i.e. exogenous gene transferring) and loss-of-function (i.e. endogenous gene silencing). List of genetic traits transferred or introgressed into plants and animals in the last two decades. Concepts of gene flow and genome fusion by means of genetic manipulations at the cellular and molecular levels, respectively (e.g. transgenic individuals and somatic hybrids). Identification of newly inserted genes and expressed gene products in transgenic individuals. General discussion on the importance of risk perception and risk potential in the context of environmental and food safety. Potential advantages and actual bottlenecks associated to the use of GMOs. The rationale and methodology of the environmental risk assessment of GMOs. Overview of the different steps in the toxicity and allergenicity assessment of GMOs. Scientific concerns associated to environmental risks (i.e. horizontal gene transfer and transgene escape) and human health (e.g. toxicity and allergenicity assessment of food/feed derived from GM plants). Analysis of GMOs and genetic traceability of their food derivatives by advanced molecular tools and assays. Legal and ethical aspects related to the production of GM plants and animals, and to the commercialization of GMO-derived products. Are there alternatives to GMOs? Genomics applied to marker-assisted selection (MAS) for breeding crop plant varieties and livestock species.

Teacher CV. Gianni Barcaccia obtained the MS in Plant Genetics and Breeding in 1991 at the Agriculture Faculty of the University of Perugia. Since 1992 he spent several training periods in international laboratories of Plant Molecular Biology. In 1995 he earned the PhD title in Genetics of Plant Reproductive Systems. In 1998 he achieved the position of Researcher at the University of Padova. Since 2004 he is Associate Professor of Plant Genetics and Genomics at the School of Agriculture and Veterinary Medicine of the University of Padova. In 2012 he obtained the national qualification as Full Professor for the scientific-disciplinary area 07/E1 Agriculture Chemistry and Genetics. Since 2012 he is Vice-director of the School of Doctorate in Crop Science and Principal investigator of the Genomics Laboratory in his own Department. He is counselor of the Italian Society of Plant Genetics and member of European Association of Plant Breeding. In the last 10 years he was involved in several research projects dealing with plant reproductive systems, population genetics and molecular markers. He got published more than 80 scientific original articles and reviews on international peer-reviewed journals and several academic books and book chapters on Plant Genetics and Genomics, and Biotechnologies.

Textbooks/bibliography Barcaccia G., Falcinelli M. (2005-2013) Genetica e Genomica (Vol. 1, Genetica generale; Vol. 2, Miglioramento genetico; Vol. 3, Genomica e Biotecnologie genetiche), Liguori Editore, Napoli.

16

Harmonic analysis

Teacher: Paolo Ciatti – UniPD – paolo.ciatti@unipd.it Motivations. The purpose of this course is to give a self-contained introduction to some geometric features of harmonic analysis, related, in particular, to the outstanding problem of the restriction of the Fourier transform to a surface. The subject deals with the observation made by E. M. Stein forty years ago that it is sometimes possible to consider the restriction to a surface of the Fourier transform of a function in L^p for some p greater than or equal to 1. This phenomenon sounds paradoxical since surfaces are sets of Lebesgue measure zero, but for p not equal to 1 the Fourier transform is a priori defined only almost everywhere. Substantial progress in this theory was made in the last thirty years, but most of the techniques are still available only in the technical literature. My intent is to present an account accessible to students in mathematics and physics. Targeted audience. My intent is to present an account of the theory accessible to students in mathematics and physics of the second cycle degree (Laurea Magistrale), but motivated students of the first degree may be admitted to the lectures. The students should be familiar with basic real and functional analysis. In particular, they should have a good background in the theory of Lebesgue integration and Hilbert spaces. In any case, I intend to adapt as much as possible the course to the background and the interests of the audience. Syllabus. The lectures will start with a short review of Lebesgue spaces. After that we will introduce the Fourier transform of an integrable function in the Euclidean space, discussing its basic properties and proving the inversion formula. Then we will consider the L^2 theory of the Fourier transform, proving the Plancherel theorem, which states that the Fourier transform, preserving norms, is a rotation of L^2. To stress the geometrical point of view, we will also discuss the N. Wiener approach to the Fourier operator, showing that it is diagonal in the Hermite basis. This analysis will lead us to introduce the uncertainty principle, that will be considered in some details. We will then focus the attention on the theory of oscillating integrals, introducing the principle of stationary phase, that will be then applied to the study of the asymptotic behavior of the Fourier transforms of measures supported by surfaces. This issue will be the main tool in the study of the restriction theory of the Fourier transform, with whom we intend to conclude the course. After a short introduction to this problem, we will concentrate on the theorem of P. A. Tomas and E. M. Stein, concerning the restriction of the Fourier transform to a compact hypersurface with non-vanishing gaussian curvature. We will then show how this issue rapidly leads to existence and uniqueness results for the Schrödinger equation. Finally, we will state and discuss the famous restriction conjecture of Stein, commenting on its connection with some outstanding problem in combinatorics. Teacher CV. Undergraduate Education: Laurea in Fisica, Università di Torino,1990. Thesis directed by Prof. Tullio Regge: "Un principio variazionale per una stella non isotropa a simmetria assiale in relatività generale". Graduate Education: PhD in Mathematics, Politecnico di Torino,1995. Thesis directed by Prof. Fulvio Ricci: "Analisi armonica su di una classe di varietà pseudo-rimanniane armoniche". Academic Positions: Junior Researcher, University of New South Wales (Sydney),1996-1997. Ricercatore, Università di Padova, 1998-2008. Professore Associato, Università di Padova, 2008-present. Adjoint Professor, Dalhousie University (Halifax, Nova Scotia), 2013-present. Visiting Positions: Mittäg Leffler Institute, Spring 1996. University of New South Wales, March-April1998. Univesidad de Còrdoba (Argentina), August 2001. University of New South Wales, July-August 2000. University of New South Wales, August-September 2002. University of New South Wales, March-April 2004. Purdue University, March 2008. University of New South Wales, July-August 2012. Dalhousie University, August 2013. Textbooks/bibliography Elias M. Stein, Harmonic Analysis, Real-Variable Methods. Orthogonality, and Oscillatory Integrals, Priceton University Press.

17

Introduction to strings theory

Teacher: Stefano Giusto – UniPD – stefano.giusto@unipd.it

Motivations

String theory represents a significant theoretical extension of quantum field theory, with deep implications for both physics and mathematics. From the point of view of physics, string theory unifies in a consistent framework quantum mechanics and general relativity and provides the most promising theoretical scheme for a unified theory of fundamental interactions. At the same time string theory probably represents the richest and most complex mathematical object that has emerged from physics, having multiple connections with differential and algebraic geometry, topology, representation theory and infinite-dimensional analysis. The goal of this course is to provide a basic introduction to the classical and quantum aspects of string theory, clarifying those aspects which are essential to grasp its fundamental physical content.

Targeted audience

The course is aimed at both physicists and mathematicians. Familiarity with classical physics and basic special relativity will be assumed. The essential notions of quantum mechanics relevant for the extension to string theory will be briefly reviewed.

Syllabus

Reminders of special relativity, electromagnetism, gravitation and their generalization to space-times with extra dimensions.The classical relativistic bosonic string: Nambu-Goto and Polyakov actions, equations of motion, boundary conditions for open strings, mode expansion, conserved currents, gauge invariance and constraints. The relativistic string in the light-cone gauge. Lightning review of quantum mechanics: quantization of the relativistic particle and the harmonic oscillator. Quantization of the relativistic bosonic string: covariant and light-cone quantizations; open strings and the dynamics of D-branes; the spectrum of closed strings and the emergence of gravity. Compactification and T-duality. String amplitudes. A qualitative overview of the superstring, low energy effective actions (supergravity) and applications to the study of black holes.

Teacher CV. Researcher at the University of Padua. Master (Laurea), U. Genoa,1994, 110/110 cum laude. Ph. D. in Physics: U. Genoa, 1999. Academic Positions: Post-doc, Harvard University, USA, 1999; Research contract, U. Lecce, Italy, 2000; Research contract, U. Genoa, Italy, 2000-03; Post-doc, The Ohio State University, USA, 2003-06; Post-doc, U. Toronto, Canada, 2006-07; Post-doc, IPhT, Saclay, France, 2007-09; Post-doc, LPTHE, Paris 6, France, 2009-10; Researcher, U. Genoa, Italy, 2010-11. Teaching: Theoretical Physics (Teaching assistant), U. Genoa, 2000-2003; Theoretical Relativistic Physics (Teaching assistant), U. Padua, 2010-11; String Theory, Ph. D. in Physisc, U. Padua, 2011-12; Electromagnetic Fields (Main Teacher), U. Padua, 2011-2014. Research topics: Topological Field Theory and Strings; Non-commutative field theories; Open String Field Theory; Black Holes in String Theory; Exact solutions in supergarvity. Textbooks/bibliography B. Zwiebach, "A First Course in String Theory" D. Tong, "Lectures on String Theory"

18

Philosophy of science

Teachers: Pierdaniele Giaretta - UniPD, Giulio Giorello - UniMI, Telmo Pievani – UniPD Pierdaniele.giaretta@unipd.it, dietelmo.pievani@unipd.it, giulio.giorello@unimi.it Motivations. Philosophy of science is a privileged field for an interdisciplinary course devoted to basic issues like the scientific methodologies in natural and social sciences, the models of explanation, the nature and development of scientific theories, the analysis of scientific concepts and terminologies, the social and ethical impact of science. Students admitted to higher education with different competencies (ranging from physics to life sciences, from philosophy to economy) could find an useful introduction to the epistemology of XXI century and its updated tools. This should improve their historical and critical view about the specific disciplines they are studying, and promote cross-references and relationships. The course will be based on recent case-studies in scientific literature, in order to be strictly related to the reality of current researches. The tree voices of the course will cover general philosophy of science (kinds of explanations), philosophy of physics and philosophy of biology. Targeted audience. Students involved in higher education programmes referring to natural sciences (physics, chemistry, biology, biomedicine, Earth sciences), mathematics, social sciences and economy, philosophy, history. Researchers and teachers interested in interdisciplinary exchanges and interactive discussions of case-studies in philosophy of science. Syllabus. The introductory part of the course (prof. Pierdaniele Giaretta) will be devoted to the presentation of the so-called “received view” of the notion of scientific explanation, to the problems it currently presents, to the partially alternative conceptions of Salmon and Kitcher, and then to the more radically alternative vision proposed by B. Van Fraassen (which however, at least from a historical point of view, is located between Salmon’s and Kitcher’s one). The subsequent developments will be mentioned. The overall aim is to highlight the difficulty of producing general models of explanation, but also the unacceptability of the waiver to have at least some form of explanatory relevance, not entirely determined by contextual, contingent and social factors. In order to illustrate this narrow passage between the multiplicity of models of explanation and the need for explanatory relevance, the next two parts of the course will be focused respectively on biological sciences (prof. Telmo Pievani) and physical sciences (prof. Giulio Giorello). In the first one, we will see the uniqueness of contemporary biology, as increasingly evident because of its evolutionary core, the ability to incorporate new features into a coherent research program, the mixture of quantification and qualitative models, generalizations and case studies. We will discuss the application of evolutionary models in psychology and the social sciences as well. In the second one, the concepts of probability and the relationships between mathematic language and physics will be the main issues. Teachers CV. Pierdaniele Giaretta is full professor of Logics and Philosophy of Science at the University of Padua, Department of Philosophy, Sociology, Education and Applied Psychology. His main lines of research are the history of logics, philosophy of logics, intuitionistic logics, analytic ontology, logics and psychology, kinds of explanations, philosophy of medicine. Giulio Giorello is full professor of Philosophy of Science and Epistemology of Social Sciences at the University of Milan, Department of Philosophy. His main lines of research are the philosophy of mathematics, relationships between physics and mathematics, philosophy of probability, history of science, science and humanities. Telmo Pievani is associate professor of Philosophy of Biological Sciences and Anthropology at the University of Padua, Department of Biology. His main lines of research are the philosophy of biology, evolutionary biology, evolution and phylogeny, human evolution, history of biological thought, Charles Darwin’s heritage. Textbooks R. Campaner, M.C. Galavotti, 2012, La spiegazione scientifica. Modelli e problemi, Archetipolibri, Bologna. F.J. Ayala, R. Arp (eds.), 2010, Contemporary Debates in Philosophy of Biology, Wiley-Blackwell, Chichester (UK).

19

Nanoscience and Nanosystems Teachers: Luisa De Cola (ISIS, Strasbourg) and Fabrizio Mancin (UniPD) decola@unistra.fr, fabrizio.mancin@unipd.it Motivations Nanoscience is an emerging research field which is expected to be the basis for the next industrial revolution. Moreover nanoscience is a multidisciplinary subject bridging over the areas of Physics, Chemistry, Material Science, Engineering, Biology, and Medicine. Such feature requires the development of a multidisciplinary language and comprehension, but nanoscience is still marginally or partially treated in most Bachelor curricula in the Science area. In particular, students may be confused about the correlations about nanosystems properties, synthesis and applications in different fields. The goal of the present course is to introduce students to nanoscience in a comprehensive and multidisciplinary manner. While keeping chemistry and material sciences aspects at a level suitable for first-year undergraduate students, emphasis will be given to understand the basic features of nanomaterials, the self-assembling concept, the nanosize-related properties and their applications in different fields. Targeted audience The course targets the Natural Science Class of the Galileian School of the University of Padova, including students in Physics, Mathematics, Chemistry, Engineering, Biology, and Medicine. The ideal audience is supposed having been exposed to an introductory course of general Chemistry. Syllabus What is a nanoparticle? Why it should not exist? Why it exists? The bottom-up approach by self-organization: from single molecules to nanoscale by self-assembly (intermolecular forces, analytical tools for characterization, thermodynamics and kinetic aspects). Micelles, liposomes, polymeric capsules, gels, DNA nanotechnology. Nanomedicine, the application of nanosystems to diagnosis and therapy. The journey of a nanoparticle in a living organism: the protein corona, the organism reaction, the biological barriers, the interaction with the target. Existing nanodrugs: protein nanoparticles, biodegradable polymers, liposomes for therapeutic applications. The development of a new application: lipid nanoparticles for siRNA delivery. Hard materials nanosystems. Confinement effects. Design and tools. Porous silica materials. Porous titania and applications of porous systems. Metal nanoparticles: biomedical application. Superparamagnetic nanoparticles: biomedical application. Teacher CV Fabrizio Mancin is Assistant Professor in Organic Chemistry at the Chemical Sciences Department of the University of Padova. He is co-author of about 70 articles in international journals, 5 book chapter and 1 patent application. He teaches Organic Chemistry for the Bachelor degree in Material Sciences, Nanobiotechnology for the Master degree in Industrial Biotechnology and Supramolecular Chemistry for the Master degree in Chemistry. His research interests are in the field of supramolecular catalysis and sensing, self-organization in nanosystems and nanomedicine. Luisa De Cola is Full Professor (Class Exceptionnelle) and AXA chair of Supramolecular and Biomaterial Chemistry at the Institut de Science et d'Ingénierie Supramoléculaires, ISIS, of the University of Strasbourg, (France). She is also adjunct scientist at the Karlsruher Institut für Technologie, KIT (Germany). She has published 300 papers and filed 30 patent. Her research activity is focused in 2 main research areas: a) luminescent and electro-luminescent materials for optical and electroluminescent devices; b) nanomaterials for imaging diagnostics and therapy. Textbooks/bibliography Rob Burgess, Understanding Nanomedicine: An Introductory Textbook, CRC Press 2012 Jonathan W. Steed, David R. Turner, Karl Wallace, Core Concepts in Supramolecular Chemistry and Nanochemistry, Wiley, 2007 Hierarchically Structured Porous Materials Eds. B.-L. Su, C. Sanchez, X.-Y. Yang, Wiley, 2012 L. Cademartiri, G.A. Ozin Concepts of Nanochemistry Wiley, 2009