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

September 23rd Organizational Meeting

September 30th Hanfeng Li, SUNY at Buffalo

Hilbert C*-modules admitting no frames

Abstract: It is a consequence of Kasparov's stabilization theorem that every countably generated

Hilbert C*-module over a unital C*-algebra has frames. I will show that this fails in general for

arbitrary Hilbert C*-modules.

October 14th Jon Kraus, SUNY at Buffalo

A generalization of Hilbert C*-modules

Abstract: We will discuss a generalization (due to David Blecher) of Hilbert C*-modules where

the C*-algebra is replaced by an arbitrary operator algebra (a norm closed subalgebra of the

bounded operators B(H) on a Hilbert space H). The generalization is based on a characterization

of Hilbert C*-modules that does not involve inner products (or adjoints). We will also discuss Hilbert

W*-modules and their generalization (where the W*-algebra is replaced by an operator algebra

which contains the identity operator and is closed in the weak* topology of B(H)).

October 28th Quanlei Fang, SUNY at Buffalo

Commutators and localization on the Drury-Arveson space

Abstract: Let f be a multiplier for the Drury-Arveson space H

denote the coordinate functions.We show that for each 1≤ i ≤ n, the commutator [M

belongs to the Schatten class C

November 4th Jingbo Xia, SUNY at Buffalo

Defect operators associated with submodules of the Hardy module

Abstract: Let H

Hilbert module over the ball algebra A(B). Let M

to the multiplication by the coordinated functions. Each submodule Μ⊂H

the module operators Z

commonly believed, but never previously proven result: whenever M≠{0}, the sum of the commutators

[Z

does not belong to the Schatten class C

November 18th Byung Jay Kahng, Canisius College

Some remarks on duality in the locally compact quantum group setting

Abstract: In abstract harmonic analysis, among the most important result is the Pontryagin duality,

which holds at the level of locally compact abelian (LCA) groups. Also, at the LCA group level,

the notion of Fourier transform is defined. For further generalization, we consider the category of

quantum groups, where Pontryagin-type, self-duality holds. Our quantum groups are locally compact

quantum groups, in the C*-algebra or von Neumann algebra framework.

By using the notion of the multiplicative unitary operators and the generalized Fourier transform, we

can enhance our understanding of the duality picture at the quantum group level. In particular, we will

consider a case of a certain coalgebra deformation of the quantum double, and its dual counterpart.

December 16th Wen Huang, University of Science and Technology of China

Stable sets and unstable sets in positive entropy systems

Abstract: Stable sets and unstable sets of a dynamical system with positive entropy are investigated.

It is shown that in any invertible system with positive entropy, there is a measure-theoretically “rather big”

set such that for any point from the set, the intersection of the closure of the stable set and the closure

of the unstable set of the point has positive entropy. Moreover, for several kinds of specific systems,

the lower bound of Hausdorff dimension of these sets is estimated. Particularly the lower bound of the

Hausdorff dimension of such sets appearing in a positive entropy diffeomorphism on a smooth Riemannian

manifold is given in terms of the metric entropy and of Lyapunov exponent.