Analysis   Seminar    

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

February 1st             Hanfeng Li,     SUNY at Buffalo
                         Entropy and
L2-torsion, Part I

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 L2-torsion of M are defined. I will
                         discuss the relation between the entropy and the L2-torsion, and indicate how this confirms the conjecture of Wolfang Luck that the universal
                         covering space of any aspherical connected finite CW-complex with nontrivial amenable fundamental group has trivial L2-torsion. This is joint
                         work with Andreas Thom.

February 8th            
Hanfeng Li,     SUNY at Buffalo
                         Entropy and
L2-torsion, Part I

February 22nd            Jingbo Xia,    SUNY at Buffalo
Invariant subspaces for certain finite-rank perturbations of diagonal operators

                         Abstract: Suppose that {ek} is an orthonormal basis for a separable, infinite-dimensional Hilbert space H. Let D=∑k=1λkek⊗ek be a bounded
                         operator that is diagonal with respect to the orthonormal basis {ek}. Consider the operator
                         Improving a result of Foias, Jung, Ko, and Pearcy of 2007, we show that if the vectors u1, …, un and v1, …, vn satisfy an l1-condition with
                         respect to the orthonormal basis {ek}, and if T is not a scalar multiple of the identity operator, then T has a non-trivial hyperinvariant
                         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

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                
Anthony Weston,    Canisius College

                          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

                          Abstract: I will construct a class of metric measure spaces starting from  base metric measure spaces each with a Dirichlet form. The
                          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.

April 26th                Jesse Peterson,   Vanderbilt University
(Thursday, Colloquium)   

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