Analysis   Seminar    


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

                            

September  18-20              Guoliang Yu,   Texas A&M University
(Myhill Lectures)                            

September 27th                Mehrdad Kalantar,   University of Houston
                              Boundary actions and applications to rigidity problems in operator algebras

                              Abstract: We show how boundary actions in the sense of Furstenberg can be applied to some rigidity problems in operator algebras. In contrast to previous    
                              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                   Yi Wang,       Texas A&M University
                              On the p-essential normality of principal submodules of the Bergman module on strongly pseudoconvex domains

                              Abstract: We show that under a mild condition, a principal submodule of the Bergman module on a strongly pseudoconvex domain, generated by a holomorphic
                              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                  Jianchao Wu,    Penn State University
                              Dimensions in topological dynamics and crossed product C*-algebras

                              Abstract: C*-algebras are a kind of operator algebras that are tailored to describe noncommutative (i.e., quantum) topological spaces through analytical
                              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                  Kate Juschenko,   Northwestern University
                              Cycling amenable groups and soficity

                              Abstract: I will give introduction to sofic groups and discuss a possible strategy towards finding a non-sofic group. I will show that if the Higman group
                              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                  Alexandru Chirvasitu,   SUNY at Buffalo
                              Rigidity and softness for discrete quantum groups

                              Abstract: Discrete quantum groups are the noncommutative geometer's analogue of ordinary groups, and are defined mathematically as Hopf algebras satisfying a
                              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