Functional Analysis Seminar
20172018
Time  Location  Seminar Organizers 

Tuesday — 11:00am–12:00pm  AP&M 6402 (unless otherwise specified)  Adrian Ioana (aioana@ucsd.edu) Todd Kemp (tkemp@ucsd.edu) 
Fall 2017
Date  Speaker  Title + Abstract 

October 9 
Christopher Schafhauser
York University 
Subalgebras of AFAlgebrasA longstanding open question, formalized by Blackadar and Kirchberg in the mid 90's, asks for an abstract characterization of C$^*$subalgebras of AFalgebras. I will discuss some recent progress on this question: every separable, exact C$^*$algebra which satisfies the UCT and admits a faithful, amenable trace embeds into an AFalgebra. Moreover, the AFalgebra may be chosen to be simple and unital with unique trace and the embedding may be taken to be tracepreserving. Modulo the UCT, this characterizes C$^*$subalgebras of simple, unital AFalgebras. As an application, for any countable, discrete, amenable group $G$, the reduced C$^*$algebra of $G$ embeds into a UHFalgebra. 
November 6 
David Jekel
UCLA 
An Elementary Approach to Free Gibbs Laws Given by Convex PotentialsWe present an alternative approach to the theory of free Gibbs laws with convex potentials developed by Dabrowski, Guionnet, and Shlyakhtenko. Instead of solving SDE's, we combine PDE techniques with a notion of asymptotic approximability by trace polynomials for a sequence of functions on $M_N(\mathbb{C})_{sa}^m$ to prove the following. Suppose $\mu_N$ is a probability measure on on $M_N(\mathbb{C})_{sa}^m$ given by uniformly convex and semiconcave potentials $V_N$, and suppose that the sequence $DV_N$ is asymptotically approximable by trace polynomials in a certain sense. Then the moments of $\mu_N$ converge to a noncommutative law $\lambda$. Moreover, the free entropies $\chi(\lambda)$, $\underline{\chi}(\lambda)$, and $\chi^*(\lambda)$ agree and equal the limit of the normalized classical entropies of $\mu_N$. An upcoming paper will use the same techniques to obtain transport maps from $\lambda$ to a free semicircular family as the limit of transport maps for the matrix models $\mu_N$. 
November 8 1pm in APM 6402 
Pooya Vahidi Ferdowsi
Caltech 
TBA

November 13 
Scott Atkinson
Vanderbilt University 
TBA

November 15 
Anush Tserunyan
UIUC 
TBA 
December 4 
Daniel Hoff
UCLA 
TBA

Winter 2018
Date  Speaker  Title + Abstract 

January 15 
Artem Pulemotov
University of Queensland 
(Joint with Geometry Seminar)

Spring 2018
Date  Speaker  Title + Abstract 
