Unless specified, all seminars are Wednesday 4-5pm at 250 Math Building.

January 28th Hanfeng Li, SUNY at Buffalo

Turbulence, representations, and trace-preserving actions

Abstract: I will give criteria for tubulence in spaces of C*-algebra representations, and indicate

how this helps to establish results of nonclassifiability by countable structures, for group actions

on a standard atomless probability space and on the hyperfinite II

with David Kerr and Mikaël Pichot.

February 11th David Sherman, University of Virginia

Relative operator theory

Abstract: Many statements from operator theory still make sense when B(H) is replaced with

a different von Neumann algebra. Some classical theorems generalize perfectly, others fail miserably;

most valuable are those whose truth depends on the structure of the von Neumann algebra. I will

survey several recent results and open problems in this "relative" operator theory.

March 4th

Schatten class Toeplitz and Hankel operators on the Segal-Bargmann and Bergman spaces

Abstract: We discuss and compare Schatten p class membership for 0 < p < ∞ of Toeplitz and

Hankel operators on the Segal-Bargmann space and the Bergman space of the unit ball in C

In particular, we discuss the cut-off phenomenon that occurs when characterizing Schatten p class membership

of Toeplitz and Hankel operators on the Bergman space of the unit ball, but which does not occur

when characterizing Schatten class Toeplitz and Hankel operators on the Segal-Bargmann space.

This is partly joint work with K. Zhu.

March 11th Mikaël Pichot, IPMU, University of Tokyo

(Canceled) Isoperimetry and dynamical systems

Abstract: I will describe the behavior of isoperimetric type constants for certain measurable

dynamical systems. This is joint work with R. Lyons and S. Vassout.

March 18th Shuzhou Wang, University of Georgia

Simple Compact Quantum Groups

Abstract: In the theory of compact quantum groups, two classes of examples have been

intensively studied. The first are obtained as various deformations of compact Lie groups

and were main objects of study in the theory of quantum groups in the later 1980s and 1990s.

The second are constructed as universal objects in appropriate categories of quantum

transformation groups and are in general not obtainable as deformations of compact Lie groups.

The latter class of quantum groups have been focus of study in recent years. Because of

the existence of the latter class of quantum groups, it is a fundamental problem to classify

simple compact quantum groups.

In this talk, I will explain the notion of simple compact quantum groups and

indicate how to prove simplicity of (1) the universal orthogonal groups, (2) the quantum

automorphism group of finite spaces and (3) deformations of simple Lie groups.

March 25th Xiaoqing Li, SUNY at Buffalo

A spectral mean value theorem for GL(3) automorphic forms

Abstract: Assuming the Langlands functoriality conjectures, it is known the first Fourier coefficient

of a Maass form on GL(n) (normalized such that its L

without assuming the Langlands functoriality conjectures, we will prove the essentially boundedness

of the first Fourier coefficient of a GL(3) Maass form is true on the average.

April 1st Quanlei Fang, SUNY at Buffalo

Schatten class membership of Hankel operators on the unit sphere, I

Abstract: Let H

feature of this investigation is that we consider all possible symbol functions f in the L

We completely determine the membership of H

H

the membership H

April 8th Jingbo Xia, SUNY at Buffalo

Schatten class membership of Hankel operators on the unit sphere, II

April 22nd Erik van Erp, University of Pennsylvania

Contact structures of higher codimension: an analytic perspectives

Abstract: A contact manifold is a manifold equipped with a codimension one distribution that satisfies

a certain "maximal non-integrability" condition. Contact manifolds appear naturally as boundaries of

complex domains. Operators of interest on contact manifolds are the tangential Cauchy-Riemann operator

and the Szego projector. The Heisenberg calculus is the appropriate pseudodifferential calculus for

the analysis of these operators.

We propose a simple condition on a distribution of higher codimension
that generalizes this geometric structure.

Geometrically, our condition is satisfied, for example, for the Carnot
Caratheodory structure on the boundary

of hyperbolic space, or for a natural codimension 3 distribution on the
boundary of domains in hyperkahler manifolds.

We characterize these higher codimension "contact structures" in terms
of a property of the appropriate

Heisenberg calculus. We construct a natural generalization of the
tangential CR operator, and prove that

it has similar spectral properties as its classical counterpart. There
is a Szego projector, and the Boutet de Monvel

index theorem holds for the associated Toeplitz operators.