Organizer: Adrian Ioana (aioana@ucsd.edu)
Unless specified otherwise, talks will be held in AP&M 6402 from 11:00am-11:50am on Tuesdays.
September 29 no seminar
October 6
Speaker: Hui Tan (UCLA)
Title: A class of II$_1$ factors without non-trivial crossed product decompositions
Abstract: The crossed product is a fundamental construction of II$_1$ factors, and a natural question is whether every separable II$_1$ factor arises from a noncommutative dynamical system in this way. I will discuss joint work with Adriana Fernández Quero and Adrian Ioana in which we construct the first separable II$_1$ factors that cannot be decomposed as $B\rtimes G for any trace-preserving action of any countably infinite group $G$ on any tracial von Neumann algebra $B$ . Our approach relies on a rigidity phenomenon for embeddings. Specifically, for the constructed factors, all embeddings into their tensor products come from the canonical embeddings, which is incompatible with the comultiplication associated to an infinite crossed product decomposition.
October 13 no seminar
October 20
Speaker: Ching Wei Ho (UCSD)
Title: Free multiplicative random walk
Abstract: We consider the matrix random walk where the multiplicative increments are the identity plus a bi-invariant matrix, and the free random walk where the
multiplicative increments are the identity plus a R-diagonal operator. In this talk, I will first speak about the result that the limit of the empirical eigenvalue distribution of the matrix random walk as the size of the matrix approaches infinity is the Brown measure of the free random walk. Then I will speak about the result that the limit of the Brown measure of the free random walk as the number of steps approaches infinity is the lima bean law. This is joint work with Driver, Hall, Kemp, Nemish, Nikitopoulos, Parraud.
October 27
Speaker: David Gao (UC Berkeley)
Title: Non-isomorphism of reduced free group C*-algebras, via non-K-theoretic methods.
Abstract: Using a new, non-K-theoretic approach involving embedding spaces in II1 factors with plenty of freely independent Haar unitaries, we prove that the reduced free group C*-algebras for different numbers of free generators are pairwise non-isomorphic. This recovers the seminal result of Pimsner and Voiculescu with a short new proof. This talk is based on joint work with Srivatsav Kunnawalkam Elayavalli.
November 3
Speaker: Forte Shinko (UCSD)
November 10
Speaker: Yoonje Jeong (UCSD)
November 17
Speaker: Srivatsav Kunnawalkam Elayavalli (UC Berkeley)
Title:
Abstract:
November 24 TBD
December 1
Speaker: Todd Kemp (UCSD)