Analysis   Seminar    

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

February 7th                  Jingbo Xia,   SUNY at Buffalo
                              A double commutant relation in the Calkin algebra on the Bergman space

                              Abstract: Let T be the Toeplitz algebra on the Bergman space of the unit ball. We show that the image of T in the Calkin algebra satisfies the double
                              commutant relation. This is a surprising result, for it is the opposite of what happens on the Hardy space.

February 14th                 Weiran Sun,  Simon Fraser University
                              Global Well-Posedness of the Non-Cutoff Boltzmann Equation with Polynomial Decay Perturbations

                              Abstract: In this talk we will present our recent work on the global well-posedness of the non-cutoff Boltzmann equation with hard potentials. The solution
                              considered is near equilibrium where the deviation has a polynomial decay. The main step is to show a closed energy estimate for small data. This is achieved
                              by combining methods of moment propagation, spectral analysis of the linearized operator, and smoothness e ffect starting from data with weak regularity. This
                              is a joint work with Alonso, Morimoto, and Yang.                             

April 4th                     Tsan Cheng Yu,    SUNY at Buffalo
                              The Second Moments of Hecke-Maass Forms for SL(3,Z)


April 11th                    Nico Spronk,    University of Waterloo
                              Idempotents, topologies and ideals

                              Abstract: A classical theorem due to Jacobs, and de Leeuw and Glicksberg, shows that a continuous representation of a topological group G on a reflexive
                              Banach space may be decomposed into a "returning" subspace and a "weakly mixing" subspace. Furthermore, following Dye, Bergelson and Rosenblatt
                              characterized the weakly mixing vectors as those for which the closure of the weak orbit of the vector contains zero. I wish to exhibit a generalization
                              of these results, inspired, in part, by some work of Ruppert on abelian groups. I will exhibit a bijective correspondence between
                              -- central idempotents in the weakly almost periodic compactification of G,
                              -- certain topologies on G, and
                              -- certain ideals in the algebra of weakly almost periodic functions.
                              Given time, I will indicate some applications to Fourier-Stieltjes algebras.
April 18th                    Hanfeng Li,    SUNY at Buffalo
                              Garden of Eden and specification

                              Abstract: A set is finite if and only if for every map from the set to itself surjectivity is equivalent to injectivity. The Garden of Eden theorem,
                              or Moore-Myhill property, for a dynamical system refers to the equivalence between surjectivity and certain weak form of injectivity for every
                              equivariant continuous map from the underlying space to itself. I will exhibit a general GOE theorem for algebraic actions of amenable groups.

May 9th                       Rostislav Grigorchuk,   Texas A&M University
                              Group of intermediate growth, aperiodic order, and Schroedinger operators

                              Abstract: I will explain how seemingly unrelated objects: the group G of intermediate growth constructed by the speaker in 1980, the aperiodic order, and
                              the theory of (random) Schroedinger operator can meet together. The main result, to be discussed, is based on a joint work with D.Lenz and T.Nagnibeda. It
                              shows that a random Markov operator on a family of Schreier graphs of G associated with the action on a boundary of a binary rooted tree has a Cantor
                              spectrum of the Lebesgue measure zero. This will be used to gain some information about the spectrum of the Cayley graph. The main tool of investigation
                              is given by a substitution, that, on the one hand, gives a presentation of G in terms of generators and relations, and, on the other hand, defines a minimal
                              substitutional dynamical system which leads to the use of the theory of random Shroedinger operator.
                                        No special knowledge is assumed, and the talk is supposed to be easily accessible for the audience.
Past Analysis Seminar