Analysis   Seminar    


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


April 10th                    Xin Ma,   Texas A&M University
                              Paradoxical comparison and pure infiniteness of reduced crossed product C*-algebras
          
                              Abstract: In this talk, I will talk about the relation between comparison phenomenon in topological dynamical systems and pure infiniteness of the reduced crossed products. In particular, we will see that dynamical comparison implies pure infiniteness of reduced crossed product under the assumption that there is no invariant ergodic probability Borel measures. In addition, for an action which is not necessarily minimal, I will introduce a new notion called paradoxical comparison, which is a generalization of dynamical comparison in the case that there is no invariant ergodic probability Borel measures. We will see that paradoxical comparison also implies the pure infiniteness of the reduced crossed product if there are only finitely many invariant closed subsets of the action. If time permits, I will talk about more applications of paradoxical comparison.



April 17th                    Felipe García-Ramos,   Universidad Autonoma de San Luis Potosi
                              Topological hierarchy of dynamical systems with discrete spectrum
          
                              Abstract: Dynamical systems with discrete spectrum (via the Koopman L^2 operator) are simple systems from a measure theoretic perspective. Nonetheless, from a topological point of view they can exhibit a range of behaviors. Several recent results have built a hierarchy to understand the topological complexity of these systems.



April 24th                    Sebastián Barbieri,   University of British Columbia
                              How to find aperiodic subshifts on countable groups
          
                              Abstract: We will show that for any countable group G there is a non-empty, G-invariant and closed subset X of {0,1}^G on which G acts freely by translations. This was first proven by Gao, Jackson and Seward using an intricate construction. We shall present a "one page proof" which is based on a probabilistic tool: the Lovász local lemma. This is joint work with Nathalie Aubrun and Stéphan Thomassé.
                            

Past Analysis Seminar