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

August 28th

Fredholm theory and localization on metric measure spaces

Abstract

September 25th

Towards the classification of locally trivial noncommutative principal bundles

classifying space BG, and all isomorphic principal G-bundles are classified by the homotopy class of such a map. The aim of this talk is to find an

analog of this result in the realm of noncommutative topology, where instead of topological spaces and groups, we consider C*-algebras and

quantum groups respectively. First, we introduce the notion of a locally trivial noncommutative principal bundle in the setting of compact quantum

group actions on C*-algebras. Then, for a compact quantum group G, we define the C*-algebra of functions on the noncommutative classifying

space C(BG) and prove that it classifies all locally trivial noncommutative principal G-bundles.

October 2nd

A sharp inequality of Hardy-Littlewood type via derivatives

October 9th

An Estimate for Spherical Functions on SL(3,R)

when the group parameter a is restricted to a compact subset of the abelian subgroup A. In the case of SL(3,R), it improves a result by

J.J. Duistermaat, J.A.C. Kolk and V.S. Varadarajan by removing the limitation that a should remain regular. As in their work, we estimate the

oscillatory integral that appears in the integral formula for spherical functions by the method of stationary phase. However, the major difference

is that we investigate the stability of the singularities arising from the linearized phase function by classifying their local normal forms when the

parameters \lambda and a vary.

October 16th

Revisiting Arveson's Dirac operator of a commuting tuple

Abstract

every Dirac operator is associated with a commuting tuple. The Dirac operator of a commuting tuple has inspired several interesting problems in

multivariable operator theory. In this talk, we will revisit the Dirac operator and discuss some related problems.

October 23rd

Masser's conjecture on equivalence of integral quadratic forms

terms of matrices the problem asks, for given symmetric n-by-n integral matrices A and B, whether there is a unimodular integral matrix X satisfying

A=X'BX, where X' is the transpose of X. For definite forms one can construct a simple decision procedure. Somewhat surprisingly, no such procedure

was known for indefinite forms until the work of C. L. Siegel in the early 1970s. In the late 1990s D. W. Masser conjectured for n at least 3, there exists

a polynomial search bound for X in terms of the heights of A and B. In this talk we shall discuss our recent resolution of this problem based on a joint

work with Professor Gregory A. Margulis, and explain how ergodic theory is used to understand integral quadratic forms.

October 30th

Similarity invariants of essentially normal Cowen-Douglas operators and Chern polynomials

theory and a Brown-Douglas-Fillmore theorem in the Cowen-Douglas theory. More precisely, the Chern polynomials and the second fundamental

forms are the similarity invariants (in the sense of Herrero) of this class of essentially normal operators.

November 6th

Loosely embeddable metric spaces

to fields like computer vision, machine learning, the structure of networks and other such areas.

In the talk I will introduce a weaker notion of embeddability motivated by the study of "quantum symmetries" for metric spaces and Riemannian

manifolds. I will mention some results on the generic behavior of "most" compact metric spaces and list a number of open questions.

November 20th

The cyclicity of composite functions in the Hardy space over the infinite polydisc

periodic dilation completeness problem. In this talk, I will mainly concentrate on characterizing cyclic vectors in terms of composition operators.

Also, in order to study composition operators, dilation theory for doubly commuting sequence of C.0 contractions is involved.

Past Analysis Seminar