1998 - talks · moebius geometry and discuss relations with the integrable system approach to...

1998 - Talks Contact Marie Taris for details.

MATHEMATICS TALKS LIST

1998

Analysis Seminar. Monday, 8/24. 3:00, room 199

Prof. Kang-Tae Kim, Pohang Institute of Science and Technology

TBA

Wavelet Seminar. Monday, 8/31. 5:00, Room 199

Professor Victor Wickerhauser, Washington University

"The predictor corrector algorithm for the discrete wavelet transform" (Part I)

Colloquium. Thursday, 9/03. 4:00 tea, Room 200. 4:30 talk, Room 199

Professor Udo Hertrich-Jeromin, University of Berlin

"Transformations of surfaces: the Moebius geometry of CMC-1 surfaces in hyperbolic space". Host: Gary Jensen

Abstract: (joint work with Emilio Musso and Lorenzo Nicoldi) Isothermic surfaces form a large class of surfaces, containing minimal and cmc surfaces in space forms. I will give an overview on transformations of isothermic surfaces in Euclidean and Moebius geometry and discuss relations with the integrable system approach to isothermic surfaces. This setting will then be used to describe a new viewpoint on Weierstrass representations for minimal surfaces and cmc-1 surfaces in hyperbolic space, and certain other notions affiliated with these surfaces. Some remarks on discrete analogs of isothermic, minimal and cmc surfaces will be given, and the relation with tranformations of isothermic surfaces will be discussed.

Surfaces Seminar. Friday, 9/04. 4:00, Room 199

Professor Udo Hertrich-

"Isothermic surfaces: a quaternionic

Jeromin, University of Berlin

approach"

Abstract: Some technical background for the material presented in the colloquium talk will be given: I will give a short introduction to a quaternionic calculus for (4- and 3-dimensional) Moebius geometry and discuss how isothermic surfaces and transformations therof can be handled in the quaternionic setting. I will describe how the quaternionic calculus relates to the classical setting. Depending on the interests of the audience, I will go into details about cmc surfaces and their discrete analogs in Euclidean space, about Weierstrass representations for cmc-1 surfaces in hyperbolic space, or about an ansatz to define a discrete analog of the spectral transform and discrete cmc-1 nets in hyperbolic space.

Algebraic Geometry Seminar. Tuesday, 9/08. 4:00, Room 199

Professor Vladimir Masek, Washington University

"Gorenstein dimensions of modules"


Professor Ken Gross, University of Vermont

"Symmetry: some personal reflections". Host: Ed Wilson

Abstract: We will begin in a light expository style to explore the concepts of symmetry and invariance in disciplines ranging from art, architecture, nature, and poetry to the physical sciences. We will also discuss the the historical origins of rotational symmetry as well as the modern group- theoretic point of view. We will conclude with a brief introduction to the way in which symmetry considerations enter into current day cosmological speculation.

Miniconference in honor of Guido Weiss. Saturday, 9/12. 1:00, Lopata 101

Professor Aline Bonami, University d'Orleans

"Some remarks on Hankel operators"

2:30, Lopata 101 Professor Raphy Coifman, Yale University

"Computational harmonic analysis, problems and challenges"

4:00, Lopata 101 Professor Fulvio Ricci, Politecnico di

"Flag kernels, flag multipliers and Cauchy-Szego

Torino projections"

Sunday, 9/13. 9:30, Lopata 101

Professor Fernando Soria, Universidad Autonoma de Madrid

"Fourier inversion, localization and sets of divergence"

Analysis Seminar. Monday, 9/14. 3:00, Room 115

Professor Alex Schuster, Washington University

TBA

Wavelet Seminar. Monday, 9/14. 4:00, Room 199

Professor Victor Wickerhauser, Washington University

"The predictor corrector algorithm for the discrete wavelet transform" (Part II)

Algebraic Geometry Seminar. Tuesday, 9/15, 4:00, Room 199


"Gorenstein dimensions of modules" (continued)


Professor Bill Shannon, Washington University, Dept. of Internal Medicine

"Combining classification trees using maximum likelihood estimation" Host: Ed Wilson

Abstract: We propose a probability distribution for an equivalence class of classification trees (i.e. those that ignore the value of the cut points but retain tree structure). This distribution is parameterized by a central tree structure representing the true model, and a precision or concentration coefficient representing the variability around the central tree. We use this distribution to model an observed set of classification trees exhibiting variability in tree structure. We propose the maximum likelihood estimate of the central tree as the best tree to represent the set. This MLE retains the interpretability of a single tree model and has excellent generalizability. We implement an ascent search for the MLE tree structure using a dataset of 13 classification trees that predict the presence or absence of cancer based on immune system parameters.

Colloquium. Friday, 9/18, 4:00 tea, Professor Ruth "Mutually isospectral

Room 200. 4:30 talk, Room 199 Gornet, Texas Tech University, University of Kentucky

Riemann surfaces" Host: Gary Jensen

Abstract: We address the following question: given a natural number g, how many Riemann Surfaces S1,...,Sk of genus g can there be such that they all share the same spectrum of the Laplacian? It was shown by Buser that N(g) <=720g2. The problem of finding a lower bound for N(g) was addressed by R.Tse, who exhibited a sequence of isospectral sets of Riemann surfaces whose size relative to the genus grows at the rate c sqrt{g}. We dramatically improve this lower bound to g{c log{g

i}}; i.e., better than

polynomially for any power. Applications in spectral graph theory and number theory will be discussed.

Analysis Seminar, Monday, 9/21, 3:00, Room 115

Professor Richard Rochberg, Washington University

"Higher order Hankel operators, factorization in potential spaces, and polynomially bounded operators"

Wavelet Seminar, Monday, 9/21, 4:00, Room 199

Mr. Marcin Bownik, Washington University

"A characterization of affine dual frames" (Part I)

Algebraic Geometry Seminar, Tuesday, 9/22, 4:00, Room 199



Graduate Students Seminar, Tuesday, 9/23, 5:30, Room 199

Professor Renato Feres, Washington University

"A differential-geometric look at Poincare-Sternberg normal forms"


Professor John McCarthy, Washington University

"Preventing plasma meltdowns"


Mr. Marcin Bownik, Washington

"A characterization of affine dual frames" (Part II)

University




Geometry Seminar. Friday, 10/2. 4:00, Room 199

Professor Renato Feres, Washington University

"Cartan geometries and dynamics"

I'll show how simple dynamical ideas can be used in the study of general Cartan geometries.


Professor Al Baernstein, Washington University

"Extremal problems for moments of planar continua with fixed conformal centroid"


Professor Hrvoje Sikic, Washington University

"Characterization of low pass filters" (Part I)


Professor Chris Peterson, Washington University

"Gorenstein Liaison"

Minor Oral, Friday, 10/9, 1:30, Room 199

Mr. Ningping Liu, Washington University

"The jackknife and the bootstrap" Chair: Ed Spitznagel


Professor Nik Weaver, Washington University

"Differential geometry on metric spaces which are not manifolds"


Professor Guido Weiss, Washington University

"Characterization of low pass filters" (Part II)



"Gorenstein Liaison" (Continued)

Colloquium. Thursday, 10/15. 4:00 tea, Room 200, 4:30 talk, Room 199

Professor Daniele Struppa, George Mason University

"Algebraic methods in the study of the Cauchy-Fueter and related systems" Host: Steve Krantz

Abstract: The Cauchy-Fueter system is the quaternionic analogue of the Cauchy-Riemann system, and its solutions are regular functions of several quaternionic variables. This talk will show how to use algebraic methods, to obtain significant new properties of such functions, as well as to provide a concrete representation for them.


Mr. Marcin Bownik, Washington University

"Inverse volume inequalities for matrix weights"


Mr. Morten Nielsen, Washington University

"Convergence a.e. for Walsh type wavelet packet expansions"




Minor Oral Wednesday, 10/21 4:00, Room 199

Mr. Giacomo Gigante Washington University

"Spaces with an abstract convolution of measures" Chair: Guido Weiss

Algebraic Geometry Seminar Thursday, 10/22 2:30, Room 111

Professor Kenji Matsuki Purdue University

"Characterization of quotient singularities (in dimension 2) as hyperquotients"

Abstract: The seminar talk is a baby version of the classification principle of Reid-Mori of terminal singularities in dimension 3 as hyperquotients. Brieskorn classifies the quotient singularities {\Bbb C}^2/G where G is a finite subgroup of GL(2,{\Bbb C})

by classifying the groups G. Our approach is more geometrical: Utilizing the fact that the canonical cover of the quotient singularity is canonical (RDP), which is a hyper-surface singularity, we try to express it as a cyclic quotient of RDP by determining the equivariant standard form of the defining equations:

A_n:xy + z^{n+1} eA_n:x^2 + y^2 + z^{n+1} D_n:x^2 + y(z^2 + y^{n-2} eD_4:x^2 + y^3 + z^3 E_6:x^2 + y^3 + z^4 E_7:x + y(y^2 + z^3) E_8:x^2 + y^3 + z^5

We have to put the combinatorial conditions on the actions of the cyclic group and with these conditions we can recover Brieskorn's clasification in a quite elementary way. The upshot of this naive approach is that in principle this method is valid in all charateristics and one can try to classify log terminal singularities in positive characteristics ... the behavior of the canonical cover becomes more subtle and eventually we have some exotic ones in charactreistic 2 and 3. For the rest we have a similar table expressing them as hyperquotients of canonical singularities, extending the results of Artin and Lipman classifying the rational double points in positive charateristics.

Colloquium Thursday, 10/22 4:00 tea, Room 200 4:30 talk, Room 199

Professor Jennifer Schultens Emory University

"The tunnel number of a knot" Host: Rachel Roberts

Abstract: We define the notion of a knot and of the tunnel number of a knot and discuss some of its properties.

Colloquium Friday, 10/23 2:30 tea, Room 200 3:00 talk, Room 199

Professor Kenji Matsuki Purdue University

"Factorization problem of birational maps" Host: Vladimir Masek

Abstract: A map f:X->y between two (nonsingular projective) varieties is called "birational" if it induces an isomorphism between a dense open subset of X and a dense open subset of Y. This is equivalent to requiring f to induce an isomorphism of the fields of rational functions of X and Y.

I dimension 1, i.e., when X and Y are compact Riemann surfaces, the structure of a birational map is very simple: A map is birational if and only if it is a genuine

isomorphism.

In dimension 2, i.e., when X and Y are algebraic surfaces, this is no longer true. One can "blow up" a surface to obtain a birational map B:S'->S$, which is not an isomorphism. But the structure of a birational map is still not that complicated: A map is birational if and only if it is a composite of several blow ups (and blow downs).

In dimension 3 or higher, it is a long-standing conjecture that a birational map is always a composite of blow ups and blow downs. Recently, an affirmative solution to this conjecture has been given by Wlodarczyk and Morelli to a special class of birational maps called "toric birational maps".

In the talk, we will present a very simple and elegant idea of Morelli, which led to the solution of the toric factorization problem, in terms of the geometry of convex cones. We will discuss its application to a possible approach via "Toroidalization Conjecture" to the general factorization problem.

Geometry Seminar Friday, 10/23 4:00, Room 199

Professor Jennifer Schultens Emory University

"Counting arguments for the tunnel number of a knot"

Abstract: We discuss generalized Heegaard splittings and how they may be used in counting arguments involving the tunnel number of a knot.

Analysis Seminar Monday, 10/26 3:00, Room 115

Professor Jean-Pierre Leduc Washington University

"Irreducible Lie group representations: the early results and constructions"

Wavelet Seminar Monday, 10/26 4:00, Room 199

Professor Guido Weiss Washington University

"The characterization of MRA bi-orthonormal wavelets associated with general dilations and lattices"

Algebraic Geometry Seminar Tuesday, 10/27 4:00, Room 199

Professor Chris Peterson Washington University


Colloquium Thursday, 10/29

Professor Edward

"Standard error correction using the

4:00 tea, Room 200 4:30 talk, Room 199

Spitznagel Washington University

Huber/White formula"

Abstract: Sampling strategies very often include oversampling and sampling in clusters. Statistical routines ordinarily compute standard errors under the assumption of simple random sampling. They often produce underestimated standard errors and inflated rates of statistical significance when the SRS assumption is violated. While bootstrap methods produce correct standard error estimates, they require substantial amounts of computer time and programmer effort. A formula due to Huber (1967) and rediscovered by White (1980) yields an easily implemented alternative that uses only a modest amount of computer time.

This talk will be at the introductory level and will be illustrated by a reproduction (on a different data set) of Lee and Alexandra Benham's result that neurotics have higher mean income than normals.

Show Me Analysis Seminar Friday, 10/30 3:30 and 4:30 talks University of Missouri at Rolla

Professor Joyce McLaughlin Rensselaer Polytechnic Institute Professor Hans Weinberger University of Minnesota

Prof. Joyce McLaughlin "Using holographic images to solve inverse problems", 3:30 p.m. Prof. Hans Weinberger "An example of finite-time blowup produced by equal linear diffusions", 4:30 p.m.

Abstract for Joyce McLaughlin: Shine two lazers on a vibrating rectangular surface. An interference pattern appears. Each dark or light line is a level set of a mode shape. We solve the problem: Use the level set pattern to find properties of the object. Asymptotic analysis produces simple formulas that provide estimates for the unknown properties. We briefly describe the analysis and give a sample of the results.

(Reception and dinner to follow second talk from 6:00-8:00 p.m.)


Professor Victor Wickerhauser Washington University

"Some curious inequalities and their information-theoretic proofs"

Abstract: Using Hardy and Littlewood's notion of majorization of one sequence by another, we can give simple proofs of some strange inequalities relating discrete

probability densities. These can be used to compare different measures of information, or "entropies", and also to decide which of a selection of orthogonal bases gives the fastest rate of approximation in L2 norm.



"The characterization of MRA bi-orthonormal wavelets associated with general dilations and lattices" (continued)


Professor David Wright Washington University

"Formal inverse of power series"


Professor Pietro Poggi-Corradini Kansas State University

"Norm convergence of normalized iterates and the growth of Koenigs maps" Host: Al Baernstein


Professor George Kamberov Washington University

"The Willmore energy of holomorphic quaternionic line bundles"


Professor Richard Rochberg Washington University

"Carleson measures for Besov spaces"


Professor Darrin Speegle St. Louis University

"The construction of an infinite valued dimension function"


Professor Prabhakar Rao University of Missouri, St. Louis

"Vector bundles on projective spaces"


Professor Norberto Salinas University of Kansas

"Non existence of smooth global solution operators for the D-bar equation on some smoothly bounded pseudoconvex domains in C^n" Host: Nik Weaver

Abstract: We shall prove the following theorem. Theorem: Let P be the Bergman projection on a bounded smoothly bounded pseudoconvex domain W in C^n. Let Dbar be a closed extension of the standard Dbar operator on compactly supported smooth function on W. Let K (from [Ran (Dbar)]^(0,1) into [Dom(Dbar)]^(0,0)which is included in L^2(W))be the canonical cross section of Dbar, i.e. PK=0. Also, Let J, with the same domain and range spaces as K, be any linear cross section of Dbar.

Then the following two conditions are equivalent. (a) P is a smoothing operator. (b) K is a smoothing operator. Furthermore, if (c) J is a smoothing operator, then (a) holds. On the other hand, if PJ is smoothing, then (a) implies (c). The most important part of the above theorem is that (c) implies (a), in view of counterexamples of domains W where the global regularity of the Bergman projection fails already abundantly found in the literature.


Professor Anneke Bart St. Louis University

"Surface groups in some surgered manifolds"


Mr. Carlos Gil Bellosta Washington University

"Inner functions, Bloch spaces, and symmetric measures (work of Aleksandrov-Anderson-Nikolau)"

Colloquium Monday, 11/16 4:00 tea, Room 200 4:30 talk, Room 199

Professor Alexander Stokolas SUNY at Buffalo

"On the rate of almost everywhere conversions of certain integral means" Host: Guido Weiss


Professor Prabhakar Rao University of Missouri, St. Louis

"Vector bundles on projective spaces" (continued)


Professor Martin Scharlemann University of California, Santa Barbara

"Flattening graphs in 3-space" Host: Rachel Roberts


Professor Martin Scharlemann University of California, Santa Barbara

"Heegaard splittings of solvmanifolds"


Professor Steven Krantz Washington University

"Normal functions and the Lindelof principle"


TBA TBA


Professor David Wright Washington University

"Formal inverse of power series (II)"


Professor John McCarthy Washington University

"Von Neumann inequalities"


Ms. Kristi Lampe Washington University

"A counting formula for rooted coloured forests"

Colloquium Thursday, 12/3

Professor John Dean

"The simplest hyperbolic knots"

4:00 tea, Room 200 4:30 talk, Room 199

University of Michigan

Host: Rachel Roberts

Minor Oral Friday, 12/4 3:00, room 199

Mr. Dylan Retsek Washington University

"The multiplier problem for the ball" Chair: Steve Krantz


Professor John Dean University of Michigan

"Knots with small Seifert-fibered Dehn surgeries"


Professor John McCarthy Washington University

"Von Neumann's Inequality II: Cartan's theorem with bounds"



TBA


Mr. Jade Vinson Princeton University

"The Holyhedron Problem" Host: Al Baernstein

Abstact: Superimpose two tetrahedra so that the vertex of one pierces the face of another, and you will have a polyhedron for which one face is multiply connected. John Conway recently asked whether there can exist a "holyhedron" that is a polyhedron so that the interior of every face is non-simply connected.We briefly review previous attempts at solving the problem before presenting a construction of a holyhedron.

The construction relies on first building a huge excess of unused vertices over unpierced faces. These unused vertices are then traded at a large but fixed ratio for other vertices which pierce the remaining faces. When every face is pierced, a holyhedron results.

Special Wavelet Seminar Friday, 12/11 4:00 p.m., Room 199

Mr. Jade Vinson Princeton University

"Some applications of wavelets: an expository talk"

Abstract: We overview some of the current uses of wavelets in mathematics and

engineering, and try to justify the claim that wavelets are often the right basis in which to expand a function.

We introduce the basic example of compactly supported MRA wavelets and show the computer algorithm that it leads to. This can be used to compress or denoise signals or images, and we mention several improvements to the basic algorithm. Wavelet coefficients can be also used to classify function spaces and to recognize properties of function. Some operators become sparse when acting on wavelet expansions; this is useful in numerical analysis.

We briefly mention research with R. Coifman last summer (using wavelets as a classification tool) and current research with C. Fefferman, using wavelets to study turbulence.

Analysis Seminar Minor Oral Monday, 12/14 3:00, Room 115

Mr. Carlos Gil Bellosta Washington University

"Differential subordination of harmonic functions and martingales" (Work of D. Burkholder) Chair: Al Baernstein

1998 - talks · moebius geometry and discuss relations with the integrable system approach to...

Documents