Functional Analysis Seminar

2017-2018

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 AF-Algebras
A long-standing open question, formalized by Blackadar and Kirchberg in the mid 90's, asks for an abstract characterization of C$^*$-subalgebras of AF-algebras. 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 AF-algebra. Moreover, the AF-algebra may be chosen to be simple and unital with unique trace and the embedding may be taken to be trace-preserving. Modulo the UCT, this characterizes C$^*$-subalgebras of simple, unital AF-algebras. As an application, for any countable, discrete, amenable group $G$, the reduced C$^*$-algebra of $G$ embeds into a UHF-algebra.
November 6 David Jekel
UCLA
An Elementary Approach to Free Gibbs Laws Given by Convex Potentials
We 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 semi-concave 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 non-commutative 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