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

February 15th

On the essential commutant of the Toeplitz algebra on the Bergman space

March 8th

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).

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