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

February 1st Hanfeng Li, SUNY at Buffalo

Entropy and L

Abstract: Given any countable discrete group G and any countable left module M of the integral grout ring of G, one may consider the natural

action of G on the Pontryagin dual of M.Under suitable conditions, the entropy of this action and the L

discuss the relation between the entropy and the L

covering space of any aspherical connected finite CW-complex with nontrivial amenable fundamental group has trivial L

work with Andreas Thom.

February 8th Hanfeng Li, SUNY at Buffalo

Entropy and L

February 22nd Jingbo Xia, SUNY at Buffalo

Invariant subspaces for certain finite-rank perturbations of diagonal operators

Abstract: Suppose that {e

operator that is diagonal with respect to the orthonormal basis {e

T=D+u

Improving a result of Foias, Jung, Ko, and Pearcy of 2007, we show that if the vectors u

respect to the orthonormal basis {e

subspace. This is joint work with Quanlei Fang.

February 29th Huichi Huang, SUNY at Buffalo

Faithful compact quantum group actions on connected compact metrizable spaces

Abstract: All known (commutative) compact spaces admitting genuine faithful compact quantum group actions are disconnected. Goswami showed

that there is no genuine faithful quantum isometric action of compact quantum groups on the Riemannian manifold G/T where G is a compact,

semisimple, centre-less, connected Lie group with a maximal torus T and conjectured that the quantum permutations on (disconnected) finite

sets are the only possible faithful actions of genuine compact quantum groups on classical spaces. We construct faithful actions of quantum

permutation groups on connected compact metrizable spaces and disprove Goswami's conjecture.

March 7th

Ultrametrics

Abstract: In this talk I will describe how to characterize ultrametric spaces in terms of roundness, generalized roundness and strict

p-negative type. This allows a complete recovery of Lemin's scheme for isometrically embedding ultrametric spaces into Hilbert space. I will

further show that Lemin's entire embedding scheme actually carries over to any metric space that has p-negative type for some p > 2. It

turns out that ultrametricity is not really the issue. The issue is strict p-negative type. This talk will be delivered very much in the

spirit of a survey. I will be referring to multiple papers and several coauthors, including Hanfeng Li.

March 29th Vitaly Bergelson, Ohio State University

(Thursday, Colloquium) Uniform distribution, generalized polynomials and dynamical systems

Abstract: A classical theorem due to H. Weyl states that if P is a polynomial over R such that at least one of its coefficients (other

than the constant term) is irrational, then the sequence P(n), n=1,2,... is uniformly distributed mod 1. We will discuss some recent

extensions of this theorem which involve "generalized polynomials", that is, functions which are obtained from the conventional polynomials

by the use of the greatest integer function, addition and multiplication. We will explain the role of dynamical systems in obtaining these

results and discuss some of the connections with and applications to combinatorics and number theory.

April 11th Wenming Wu, Chongqing Normal University

Uncertainty principles for infinite abelian groups

Abstract: There are different uncertainty principles in quantum mechanics and mathematics. In this talk, by using the projections, I will

use the operator theory to revisit the uncertainty principle on finite cyclic groups and to discuss the uncertainty principle on the group

Z. This is joint work with Liming Ge, Jinsong Wu, and Wei Yuan.

April 25th Ben Steinhurst, Cornell University

Spectral Analysis and Dirichlet forms on Barlow-Evans Fractals

Dirichlet form on the chosen base space can then be extended to the limit space. Of particular interest is that when the construction is

performed with reasonable choices of parameters and full description of the spectrum of the Laplacian associated to the limiting Dirichlet

form is possible. I will give a brief overview of what has been possible to calculate using the spectrum of a particularly simple example of

this construction.

(Thursday, Colloquium) W*-superrigidity

Abstract: Given a free, measure preserving action of a countable group on a probability space, Murray and von Neumann constructed a finite

von Neumann algebra known as the group-measure space construction. Properties of this von Neumann algebra reflect properties of the group

action, but in general much of the information about the group action is lost. For instance, a seminal result of Connes shows that any two

free, ergodic actions of infinite amenable groups give rise to the same von Neumann algebra. Recently, examples of group actions have been

found such that the group-measure space construction completely remembers the group and the action. Such actions are termed W*-superrigid,

we will present an overview of results in this direction.

Past Analysis Seminars