Analysis   Seminar    

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

February 15th                
Jingbo Xia,    SUNY at Buffalo  
On the essential commutant of the Toeplitz algebra on the Bergman space 


March 8th                     Byung-Jay Kahng,   Canisius College
                              Invariant weights on a locally compact quantum groupoid

                              Abstract: Motivated by the purely algebraic notion of ``weak multiplier Hopf algebras'', we develop the definition of a class of locally compact quantum groupoids in the C*-algebra framework.  Existence of a certain canonical idempotent element plays an important role.  As in the quantum group case, we require left and right Haar weights but the antipode is not explicitly defined.  This class would contain all locally compact quantum groups, and form a self-dual category.

                                        In this talk, we will focus on how to formulate the left and right invariance conditions, similar to but different from the quantum group case.  We will gather some alternative forms of the invariant conditions.  Then we will explore the central roles these invariant weights play in the quantum groupoid theory, in the construction of the regular representations (in terms of certain partial isometries) and the antipode map.

                                        This is based on an on-going joint work with Alfons Van Daele (Leuven).

May 3rd                       Brandon Seward,   Courant Institute

                              Positive entropy actions of countable groups factor onto Bernoulli shifts


                              Abstract: I will show that if a free ergodic action of a countable group has positive Rokhlin entropy (or, less generally, positive sofic entropy) then it factors onto all Bernoulli shifts of lesser or equal entropy. This extends to all countable groups the well known Sinai factor theorem from classical entropy theory. A consequence of this theorem is that every positive-entropy free ergodic action of a non-amenable group satisfies the measurable von Neumann conjecture. 



Past Analysis Seminar