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

September 18-20

(Myhill Lectures)

September 27th

Boundary actions and applications to rigidity problems in operator algebras

work, we apply measurable boundaries in C*-algebra context, and topological boundaries in von Neumann algebraic setting. This is joint work with Yair

Hartman.

October 4th

On the p-essential normality of principal submodules of the Bergman module on strongly pseudoconvex domains

function defined on a neighborhood of its closure, is p essentially normal for p>n. Two main ideas are involved in the proof. The first is that a holomorphic

function defined in a neighborhood 'grows like a polynomial'. This is illustrated in a key inequality that we prove in our paper. The second concerns with

the commutators of Toeplitz operators. The idea of localization is throughout our argument.

October 11th

Dimensions in topological dynamics and crossed product C*-algebras

means. A major and rich source of C*-algebras lies in the construction of crossed products from topological dynamical systems, which has occupied a central

position throughout the history of C*-algebra theory. On the other hand, the dimension theory of C*-algebras, which studies analogs of classical dimensions

for topological spaces, is young but has been gaining momentum lately thanks to the pivotal role played by the notion of finite nuclear dimension in the

classification program of simple separable nuclear C*-algebras. The convergence of these two topics leads to the question: When does a crossed product

C*-algebra have finite nuclear dimension? I will present some recent work on this problem.

October 18th

Cycling amenable groups and soficity

were sofic, there would be a map from Z/pZ to itself, locally like an exponential map, satisfying a rather strong recurrence property. The approach to

(non)-soficity is based on the study of sofic representations of amenable subgroups of a sofic group. This is joint work with Harald Helfgott.

November 8th

Rigidity and softness for discrete quantum groups

suite of conditions that ensure they in many ways resemble group algebras of (plain) discrete groups.

In this talk I will mention various geometric and representation-theoretic concepts that transport over from discrete group theory to its quantum

analogue. These include properties that seem to suggest the discrete quantum group is ``rigid'' (such as Kazhdan's property (T)) or, at the other extreme,

"soft" (residual finiteness, soficity, etc.). The main results indicate various ways in which these properties interact.

(partly joint with Angshuman Bhattacharya, Michael Brannan and Shuzhou Wang)

Past Analysis Seminar