2000 - Talks

2000 - Talks Contact Marie Taris for details.

MATHEMATICS TALKS LIST

2000

Analysis Seminar Monday, 1/24 4:00, Room 199

Organizational Meeting

Wavelet Seminar Wednesday, 1/26 3:30, Room 199

Prof. Guido WeissWashington University

"Yet another characterization of wavelets"

Analysis Seminar Major Oral Monday, 1/31 4:00, Room 199

Ms. Cristina Draghici Washington University

"Sharp distortion of area under quasiconformal mappings in the plane" Chair: Al Baernstein

Math Club Talk Tuesday, 2/1 5:30, Room 222

Prof. Nik Weaver Washington University

"What are Boolean algebras?"


Mr. Marcin Bownik Washington University

"Justifying different atomic definitions of Hardy spaces on Rn"


Prof. Kang-Tae Kim Pohang University of Science & Technology Korea

"Characterization of the Hilbert ball by its holomorphic automorphism orbits" Host: Steve Krantz

Abstract: Well-known theorem of B.Wong and J.P.Rosay says that any bounded domain in finite dimensional complex Euclidean space with a strongly pseudoconvex boundary point at which an automorphism orbit accumulates has to be biholomorphic to the unit ball. In this talk, I will present its infinite dimensional Hilbert space analog recently obtained by Steven Krantz and myself: any bounded convex domain in a separable Hilbert space with a strongly pseudoconvex boundary point at which an automorphism orbit accumulates must be biholomorphic to the unit ball in the same Hilbert space. While the statement is strongly analogous to its finite dimensional ancestors, its proof is not. I shall discuss the techniques and related ideas and problems in the talk. The convexity condition may be curious, but there is a recent example by my student J. Byun which seems indicating that the convexity may be essential.


Prof. Darrin Speegle St. Louis University

"Supports of Fourier transforms of wavelets, wavelet sets, tsubq(x) and all that"

Colloquium Thursday, 2/10 4:00 tea, Room 200 4:30 talk, Room 199

Prof. Richard Laugesen University of Illinois, Urbana-Champaign

"Here, there, and everywhere - eigenvalues in differential equations" Host: Al Baernstein

Colloquium Friday, 2/11 4:00 tea, Room 200 4:30 talk, Room 199

Prof. Philippe Barbe Yale University

"Applied Statistics: a challenge for theoretical statisticians" Host: Steve Krantz

Abstract: In this talk I will review some problems coming from real data sets which I find particularly challenging, though not hopeless. Some are partially solved, and some are just wide open questions. If we admit that not everything in the world has a normal distribution, that the number 50 does not tend to infinity, statistics becomes the source of amazing questions. I will try to convince you that differential geometry may be useful to an economist, that algebraic topology may be useful to an historian, that Banach space operator theory may help a broker on Wall Street.

Analysis Seminar Major Oral Monday, 2/14 4:00, Room 199

Mr. Michael Jury Washington University

"The Arveson extension theorem and co-analytic models" Chair: John

McCarthy

Colloquium Tuesday, 2/15 4:00 tea, Room 200 4:30 talk, Room 199

Prof. Wing-Suet Li Georgia Institute of Technology

"Inequalities for eigenvalues of sums of self-adjoint operators" (Abstract posted in the Math Department) Host: Steve Krantz


Prof. Mitch Taibleson Washington University

"When is a Fourier series, and Why should it converge?"


Mr. Yu-Ping Wang Cardio-Vascular Image Analysis Lab Washington University School of Medicine

"A spline tour of multiscale representations"

Abstract: Scale is a basic aspect of image modeling. The Gaussian kernel has long been used in multiscale image analysis. As an improvement of classical multiscale technique, wavelets are largely due to the contribution of spline techniques. In this talk, a spline tour of multiscale analysis will be presented. We give a general framework for multiscale geometric representations using B-splines. The design of a new class of wavelets arising from image processing will be given in detail. In particular, the following computational and statistical issues will be highlighted. (a) Construction of wavelets using B-splines leads to computationally efficient algorithms. We show that for a class of wavelets, their masks can be factored into simple B-spline factors. As a result, these wavelets can be implemented using fast filter bank algorithms. (b) The analysis of statistical properties of wavelet transforms can be facilitated using B-splines. We show how the statistical properties of the class of wavelet transforms that are derived from B-splines can be easily deduced from that of the Gaussian function since it approximates the B-splines. Besides these analyses, the speaker will show how these representations can be used for practical imaging problems. Examples on seismic signal denosing, medical image enhancement will be given.

Colloquium Prof. Paul "Growth of Koenigs

Thursday, 2/17 4:00 tea, Room 200 4:30 talk, Room 199

Bourdon Washington & Lee University

eigenfunctions: an episode in the study of composition operators, recounted in words, pictures -- even movies" Hosts: Dylan Retsek and Steve Krantz


Prof. Wei-Dong Ruan Columbia University New York

"Lagrangian torus fibration of Calabi-Yau hypersurface in toric variety and mirror symmetry" Host: Sergio Fenley


Prof. Alexander Isaev Australian National University

"Characterization of hyperbolic complex manifolds by their groups of holomorphic automorphisms" Host: Steve Krantz

Abstract: Let $M$ be a connected Kobayashi-hyperbolic complex manifold of complex dimension $n$ and let $Aut(M)$ denote the group of holomorphic automorphisms of $M$. The group $Aut(M)$ can be given the structure of a real Lie group and let $d(M)$ denote its dimension. It is known that $d(M)\le n^2+2n$ and the equality only occurs when $M$ is holomorphically equivalent to the unit ball. In this talk I will characterize all $M$ for which $d(M)\ge n^2+1$. The work is joint with Steven Krantz.

Colloquium Tuesday, 2/22 4:00 tea, Room 200 4:30 talk, Room 199

Prof. Nets Katz University of Illinois at Chicago

"Sums, differences, and Besicovitch sets" Host: Al Baernstein


Mr. Mauro Maggioni Washington University

"A brief introduction to the discrete Fourier transform and applications"

Colloquium Thursday, 2/24 4:00 tea, Room 200

Prof. Kevin Scannell St. Louis

"Deformations of Riemann surfaces" Host: Rachel

4:30 talk, Room 199 University Roberts

Abstract: I will discuss two geometrically natural ways of deforming surfaces (grafting and twisting), how they are related, and how they can be used to navigate Teichmuller space. I will also discuss joint work with Mike Wolf in which grafting is used to give a new real-analytic parameterization of Teichmuller space.


Prof. John Etnyre Stanford University

"Contact geometry, topology and dynamics" Host: Sergio Fenley


Prof. Al Baernstein Washington University

"Sharp Khinchin and majorization inequalities for independent random variables uniformly distributed on balls and spheres"


Prof. Ed Wilson Washington University

"The geometry of curves in Euclidean space"


Prof. Guido WeissWashington University

TBA



"The construction of r-regular wavelets for arbitrary dilations"


Mr. Dylan Retsek Washington University

"A characterization of inner functions"


Mr. Wojtek Czaja Washington University

"Characterization of affine frames with general dilations"


Prof. Minping Qian Peking University

"The hidden Markov model, linguistics and gene finding"

4:30 talk, Room 199 University of Southern California

Hosts: Marty Silverstein and Guido Weiss


Prof. Thomas Bieske University of Arkansas

"Lipschitz extensions on the Heisenberg group" Host: Al Baernstein

Abstract: The relationship between infinite harmonic functions and G. Aronsson's concept of Absolute Minimizing Lipschitz Extensions is examined in R^n and the Heisenberg group. In R^n, Bhatthacharya, DiBenedetto, and Manfredi [1989] and Jensen [1993] proved existence-uniqueness utilizing the technology of viscosity solutions of Crandall, Ishii, and Lions [1992]. This talk extends those results to the Heisenberg group, which is the simplest non-abelian group.


Speaker TBA TBA


Prof. Steven Boyer University of Quebec Montreal

"The $SL_2(\mathbb C)$-representation theory of the fundamental groups of $3$-manifolds" Host: Rachel Roberts

Abstract: Over the last century, group theoretic methods have been used to great effect in the study of $3$-dimensional manifolds. This is not surprising as generically speaking, $3$-mainfolds are determined up to homotopy, and conjecturally up to homeomorphism, by their fundamental groups. Moreover experience shows that basic topological properties of $3$-manifolds correspond to basic algebraic properties of their fundamental group. In this talk, we describe how to think of the set of $SL_2(\mathbb C)$- representations of such a group as a complex algebraic set, and how this structure relates to the topology of the manifold. Applications and open problems will be discussed.

Geometry Seminar Friday, 3/24 4:00, Room 199

Prof. Steven Boyer University of Quebec Montreal

"Virtual Haken Dehn surgery"*

Abstract: One of the most important open problems in $3$-dimensional topology is Waldhausen's virtual Haken conjecture: any closed, connected, orientable, irreducible $3$-manifold with infinite fundamental group admits a finite cover which is a Haken manifold, that is, a cover which contains a properly embedded $2$-sided incompressible surface. The fundamental nature of this conjecture is reflected in the fact that virtual Haken manifolds are known to be topologically rigid and to admit geometric decompositions in Thurston's sense. In this talk we will take a statistical approach to the conjecture by examining how often the $3$-manifolds obtained by surgery on a knot are virtually Haken. In particular we show that if the knot admits a surgery of various particular sorts, then most other surgeries on it are virtually Haken. *Joint work with Xingru Zhang


Prof. Aimo Hinkkanen University of Illinois Urbana-Champaign

"On Nevanlinna's second fundamental theorem"

Algebraic Geometry Seminar Tuesday, 3/28 4:00, Room 199

Professor Alexander Borisov Washington University

"Convolution of measures structures and Tate's Riemann-Roch formula"

Abstract: I will show how one can use the convolution of measures structures on locally compact abelian groups to give the cohomological interpretation of Tate's Riemann-Roch formula (the Riemann-Roch formula for number fields). The theory is strongly analogous to the cohomology theory of line bundles on algebraic curves, but with cohomology groups being some particular sets with convolution of measures structures rather than the vector spaces"


Mr. Jason Pollentier Washington University

"Map coloring theorems"


Speaker TBA TBA

Algebraic Geometry Seminar Thursday, 3/30 9:30, Room 199

Prof. Lucian Badescu University of Bucharest

"Quasi-lines on projective manifolds"

UCLA


Prof. Lucian Badescu University of Bucharest UCLA

"Extending meromorphic functions in algebraic geometry" Host: Vladimir Masek

Abstract: Let Y be a closed subvariety of a complex projective manifold X. Let U be a small complex connected neighborhood of Y in X. Denote by M(U) (resp.by M(X)) the field of meromorphic functions on U (resp. on X), and consider the restriction map a:M(X)->(U). Then the following problem is discussed: under which conditions is the map a surjective? After a short history of the problem some elementary examples are presented. Then some significant results are presented, with special emphasis to the following two important cases: 1) X is a homogeneous projective variety, or 2) X=Y xY and Y is embedded in X via the diagonal embedding. Some applications will be given. The presentation is intended to be at a rather elementary level.



"Convergence of auto-covariance matrices"


Professor Mohan Kumar Washington University

"An irreducibility theorem"


Speaker TBA TBA


Prof. Robert McLean University of Missouri Columbia, MO

"Special Lagrangian submanifolds: something old and something new" Host: Quo-Shin Chi


Prof. Richard Rochberg Washington University

"Multipliers and Carleson measures for the Dirichlet space"

Minor Oral Ms. Cristina "Existence and

Tuesday, 4/11 1:00, Room 199

Draghici Washington University

uniqueness of monotone measure preserving maps" Chair: Al Baernstein


Prof. Vladimir Masek Washington University

TBA


Mr. Philip Gressman Washington University

"Equivalence relations revealed: The secrets of equivalence they don't want you to know"


Prof. Darrin Speegle St. Louis University

"Smoothing the analog of the Fourier transform of the 'Shannon wavelet' in R2 for arbitrary expansive integral matrices with determinant 2"

Undergraduate Talk Everyone Welcome Wednesday, 4/12 4:00 tea, Room 200, 4:30 talk, Room 115

Mr. Jerry Cline Former head of operations research McDonnell Douglas Corporation Visiting Lecturer Washington University

"The Galileo Mission" Host: Ron Freiwald

Abstract: The talk will be an overview of the entire mission, including some discussion of the vector mechanics involved in gravity assisted trajectories, how the science objectives of the mission influenced some of the mathematical analysis, and an update on the latest status/findings of the mission.


Prof. Gabor Francsics Columbia

"Waves on complex hyperbolic spaces" Host: Steve Krantz

4:30 talk, Room 199 University

Abstract: We investigate the spectrum of the automorphic Laplace-Beltrami operator on discrete quotients of complex hyperbolic space. This is a joint work with Peter Lax. Let $\Gamma$ be a discrete subgroup of holomorphic isometries of the complex hyperbolic space. We will consider geometrically finite subgroups of isometries, that is, we will work with subgroups that have a fundamental domain with finitely many sides. We assume that the fundamental domain is noncompact, has finite complex hyperbolic volume. The fundamental domain is allowed to have finitely many cusps of maximal rank. Under these assumptions, we prove that the spectrum of the automorphic Laplace- Beltrami operator consists of the union of a standard point spectrum and an absolutely continuous part of uniform multiplicity, which is equal to the interval $(-\infty, -n^{2}/4)$. The uniform multiplicity of the continuous part of the spectrum is equal to the number of cusps of maximal rank. The principal tools in our investigation are the complex hyperbolic wave equation with automorphic data and an explicit construction of translation representations.


Prof. Fedya Nazarov Michigan State University

"A remark on Turan's lemma"

Show Me Seminar Saturday, 4/15 UMSL

10:30 coffee 11:00-12:00 Prof. Michael Dorff University of Missouri, Rolla 12:-1:30 Lunch at Alumni House 1:30-2:30 Prof. Susan Friedlander University of Illinois at Chicago2:30-3:00 Coffee 3:00-4:00 Prof. Fedya Nazarov Michigan State University

Michael Dorff "Univalent harmonic mappings and minimal surfaces" Susan Friedlander "Instabilities in fluid motion" Fedya Nazarov "Geometric theory of matrix Muckenhoupt weights"


Prof. Nik Weaver Washington University

"Set theory and invariant subspaces"

Algebraic Geometry Seminar Prof. Vladimir TBA

Tuesday, 4/18 4:00, Room 199

Masek Washington University



"Parametrizing curves and applications"


Speaker TBA TBA



TBA


Prof. Joe Lakey New Mexico State University

"Divergence free fields and wavelets on rectangles"

Ph.D. Oral Thursday, 4/27 1:00, Room 199


"Anisotropic Hardy spaces and wavelets"Chair: Richard Rochberg

Analysis Seminar Friday, 4/28 3:30, Room 199

Mr. Xiang Fang Washington University

"On the dilation of operators"



"More about anisotropic Hardy spaces"

Ph.D. Oral Tuesday, 5/2 2:00, Room 199


"Applications of local autocovariance matrices" Chair: Victor Wickerhauser

Colloquium Thursday, 5/4

Prof. Enrico Laeng

"On the (p,p) norm of some Fourier

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

Politecnico di Milano

Multipliers" Host: Guido Weiss

Ph.D. Oral Friday, 5/5 2:00, Room 199

Mr. Zioma Rzeszotnik Washington University

"Characterization theorems and the theory of wavelets" Chair: Guido Weiss



"Multipliers and Carleson measures for the Dirichlet space, Part II"

Wavelet Talk Thursday, 6/29 3:00, Eads 204

Mr. Mathieu Picard Ecole Polytechnique

"Wavelet image compression with zerotrees"

Abstract: This is a detailed description of the Said and Pearlman SPIHT algorithm for image compression, including a discussion of efficient algorithms for fast discrete wavelet transforms and technicalities like boundary artifacts and compact coding.

Algebraic Geometry Seminar Wednesday, 9/6 4:15, Room 199

Prof. Wenhua Zhao Washington University

"On Jacobian and intersection number for affine curves in $\mathbb C^2$"

Analysis Seminar Thursday, 9/7 2:30, Lopata 201

Professor Alex Iosevich University of Missouri, Columbia

"Counting lattice points" Host: Richard Rochberg


Professor Andrzej Hulanicki University of Wroclaw Purdue University

"The Martin boundary of homogeneous manifolds of negative curvature at the bottom of the spectrum" Host: Guido Weiss

Math Club Organizational Meeting Thursday, 9/7

All interested students are

4:00, Room 222 invited

Analysis Seminar Wednesday, 9/13 11:00, Room 199

Organizational Meeting


Prof. Wenhua Zhao Washington University

"On Jacobian and intersection number for affine curves in C^2" (Continued)

Seminar Thursday, 9/14 4:00, Room 199

Prof. Demetrio Labate Washington University

"Time frequency analysis of pseudo differential operators."


Prof. Kyungho OhUMSL

"Mirror Symmetry-Physics"


Prof. Nets Katz Washington University

"Advanced sums and differences"

Colloquium Thursday, 9/21 4:00 tea, Room 200, 4:30 talk, Room 199

Prof. Matt Gursky Princeton University

"Some parallels between geometry in two and four dimensions." Host: Gary Jensen

Abstract: The geometry of surfaces is distinguished by its relationship to classical complex analysis, and is therefore quite special. Nevertheless, there are some features of geometry in four dimensions which exhibit a parallel with two dimensions. In this talk we hope to describe them.

Geometry Seminar Friday, 9/22 4:00, Room 199

Prof. Matt Gursky Princeton University

"An equation of Monge-Ampere type arising in comformal geometry."

Minor Oral Friday, 9/22 3:00, Room 199

Kwok-Pun Ho "On spaces of homogeneous type" Chair: Guido Weiss

Minor Oral Monday, 9/25 2:00, Room 199

Brody Johnson

"Biorthogonal Wavelets: A Theoretical Approach" Chair: Guido Weiss

Minor Oral Monday, 9/25 3:00, Room 199

Mauro Maggioni

"Biorthogonal Wavelets II: regularity and constructions." Chair: Guido Weiss


Undergraduate Missaka Warusawitharana Washington University

"Moving knight-like pieces on a rectangular chessboard."


Prof. John McCarthy Washington University

"Qualitative properties of Pick interpolations"



"Mirror Symmetry-SYZ conjectures"

Undergraduate Math Club Tuesday 10/3 5:30, Room 222

Prof. Rachel Roberts Washington University

"Recognizing the unknot"


Al Baernstein Washington University

"The Stretch Conjecture"

Algebraic Geometry Seminar Wednesday, 10/4 4:15, room 199


"Homological mirror conjectures according to Kontsevich"

Colloquium Thursday, 10/5 4:00 tea, Room 200, 4:30 talk, Room

Prof. Susan Friedlander University of

"The Ubiquity of Fluid Instability" Host: Nets Katz

199 Illinois



"Homological mirror conjectures according to Kontsevich"


Prof. David Blecher University of Houston

"Multipliers, noncommutative M-structure and applications"

ABSTRACT: Multiplier algebras of general operator spaces were introduced by the author in 1999 who used them to strengthen some theorems characterizing some of the basic algebraic structures that are of interest to operator algebraists. In 2000, we found a deeper characterization of these multipliers in joint work of the author, Effros and Zarikian. We give some applications due to the author, such as a characterization of dual operator algebras. We also discuss briefly some aspects of our joint prospect-which mostly concerns "1-sided" M-ideals. We will start from scratch assuming no familiarity with the subject, or with operator space theory. This will be a survey talk.

Special Algebra Seminar Thurs, 10/26 11:00, Room 111

Prof. Peter Russell University of Houston

"Affine surfaces with a large automorphism group"


Prof. David Blecher University of Houston

"Operator Spaces- a 'generalization of functional analysis'" Host: Nik Weaver

ABSTRACT: Functional analysis has had as some major strands: "Banach space theory", "Operator theory on a Hilbert space", "Operator Algebras". However, the twain rarely met, i.e. if you look at a basic text on Banach space theory, and a basic text on operator algebras, there is VERY little overlap. Recently a powerful theory has developed which builds a big bridge between the two. "Operator Spaces" may be viewed as a new category, which in a good sense is a bigger category than "Banach spaces", which is more suited to problems from "Operator Algebras". Obviously in an hour, one cannot say much; but we hope to give some flavor, and briefly discuss some examples of the new perspective. The talk will be suitable for grad students-and we will define pretty much all the terms we need.

Colloquium Friday, 10/27

Prof. Peter RussellMcGill University

"Affine spaces, exotic affine spaces,

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

and their automorphisms." Host: David Wright



"Interpolation and Corona theorems for algebras associated with Besov Spaces"

Analysis Seminar Friday, 11/3 4:00, Room 199

Prof. Carlo Morpurgo University of Missouri-Columbia

"Rearrangement inequalities and equalities for multiple integrals, with applications and conjectures." Host: Al Baernstein


Prof. Steve Hofmann Univeristy of MO-Columbia

"Recent progress on the square root problem of Kato" Host: Nets Katz

Algebraic-Geometry Seminar Wednesday, 11/8 4:15, Room 200

Kyungoh Oh UMSL

Mirror Symmetry Host: Mohan Kumar


Alexander Solynin Russian Academy of Sciences, St. Petersburg Texas Tech University

"Minimal area problems in conformal mapping" Host: Al Baernstein

ABSTRACT: We shall discuss some minimal area problems in standard classes of conformal mappings; i.e., we shall deal with the question of minimizing the Dirichlet integral among analytic functions that are subject to certain constrains. This talk is based on our recent results joint with Dov Aharonov and Harold Shapiro.


Prof. Nets Katz Washington University

"On the Banach Tarski paradox"

Analysis Seminar Prof. Joe Diestel TBA

Wednesday, 11/15 11:00, Room 199

Kent State University and UMC

Host: Al Baernstein

Showme Analysis Seminar Saturday, 11/18 University of Missouri-Rolla, 1:30, 3:00, and 4:30. Dinner to follow at Zeno's Steakhouse.

Speakers: Christopher Jones, Brown University Michael Renardy, VA Tech and Nets Katz, Washington University. (Not listed in order of speaking)

Host: University of Missouri-Rolla


Michael Jury Washington University, Mathematics Graduate Student

"Invariant subspaces and inner multipliers in reproducing kernel Hilbert spaces."


Prof. Emily Hamilton Emory University

"Subgroup Separability of 3-Manifolds" Host: Rachel Roberts

ABSTRACT: Let H be a subgroup of a group G. H is separable in G if, given any element g \in G \ H, there is a finite index subgroup K \subset G such that H \subset K but g \notin K. A group G is supgroup separable if every finitely generated subgroup of G is separable in G. Subgroup separability is a powerful property. It has applications in group theory and geometric topology. In group theory, it is linked to the solution of generalized word problems. In geometric topology, it is the traditional group-theoretic tool used to decide if a given immersion in a manifold M will lift to an embedding in a finite covering of M. In this talk we describe positive and negative results on subgroup separability of fundamental groups of 3-manifolds. Moreover, we examine how subgroup separability behaves with respect to amalgamated products.


Prof. Izabella Laba University of British Columbia

"An algebraic approach to the spectral set conjecture" Host: Nets Katz

ABSTRACT: In 1974, Fuglede conjectured that a domain E in R^N tiles R^n by

translations if and only if L^2(E) admits an orthogonal basis of exponentials. Subsequent research has revealed connections to deep open problems in algebra and number theory. The purpose of the talk will be to discuss these connections and to present some recent partial results supporting the conjecture.

Major Oral Tuesday, 12/12 2:00, Room 199

Lynn Apfel "Wolff's Proof of the Corona Theorem"


Dylan Retsek Washington University, Mathematics Graduate Student

"Classical Theorems on Logmodular Algebras"

Documents

2000 - Talks