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Linear Analysis Seminar

Fall 2017

Date:September 1, 2017
Time:4:00pm
Location:BLOC 220
Speaker:Gilles Pisier, TAMU
Title:Completely Sidon sets in discrete groups

Date:September 8, 2017
Time:4:00pm
Location:BLOC 220
Speaker:Gilles Pisier, TAMU
Title:Completely Sidon sets in C*-algebras

Date:September 22, 2017
Time:4:00pm
Location:BLOC 220
Speaker:Amudhan Krishnaswamy-Usha, TAMU
Title:Nilpotent elements of operator ideals are single commutators
Abstract:Pearcy and Topping asked in '71 if every compact operator can be written as a single additive commutator [B,C]=BC-CB of compact operators. While the general problem is still open, we show that every nilpotent operator in an operator ideal is a single commutator of operators from some power of the operator ideal; where the exponent depends on the degree of nilpotency. This is joint work with Ken Dykema.

Date:September 29, 2017
Time:4:00pm
Location:BLOC 220
Speaker:Scott LaLonde, University of Texas at Tyler
Title:Fell bundles: Unifying C*-algebras associated to groupoids
Abstract:Fell bundles provide one with an abstract notion of groupoid actions on C*-algebras. As a result, they provide a unifying framework in which to study many of the C*-algebras that are often associated to groupoids, including the groupoid C*-algebra, groupoid crossed products, and twisted versions of both constructions. We will discuss some recent work on Fell bundles, including a powerful stabilization result of Ionescu, Kumjian, Sims, and Williams that relates an arbitrary Fell bundle to a canonical groupoid crossed product. We focus on some consequences of this theorem in the context of nuclearity and exactness for Fell bundle C*-algebras, as well as some connections to exact groupoids and groupoid extensions.

Date:October 13, 2017
Time:4:00pm
Location:BLOC 220
Speaker:Mehrdad Kalantar, University of Houston
Title:Superrigidity relative to subgroups
Abstract:We present several ergodic theoretical and operator algebraic superrigidity results for discrete groups relative to their subgroups. These results are obtained by analyzing the restriction of boundary actions to subgroups. This is joint work with Yair Hartman.

Date:October 27, 2017
Time:4:00pm
Location:BLOC 220
Speaker:Michael Brannan, TAMU
Title:Amenable quantum groups are not always unitarizable
Abstract:A well-known theorem of Day and Dixmier from around 1950 states that if G is an amenable locally compact group, then any uniformly bounded representation of G on a Hilbert space is similar to a unitary representation. In short, amenable groups are ``unitarizable''. In this talk, I will focus on the question of whether a version of the Day-Dixmier unitarizability theorem holds in the more general framework of locally compact quantum groups. It turns out that the answer to this question is no: In joint work with Sang-Gyun Youn (Seoul National University), we show that many amenable quantum groups (including all Drinfeld-Jimbo-Woronowicz q-deformations of classical compact groups) admit non-unitarizable uniformly bounded representations.

Date:November 4, 2017
Time:09:00am
Location:U. Houston
Speaker:Brazos Analysis Seminar
Title:Brazos Analysis Seminar
Abstract:https://sites.google.com/site/brazosanalysisseminar/

Date:November 5, 2017
Time:09:00am
Location:U. Houston
Speaker:Brazos Analysis Seminar
Title:Brazos Analysis Seminar
Abstract:https://sites.google.com/site/brazosanalysisseminar/

Date:November 10, 2017
Time:4:00pm
Location:BLOC 220
Speaker:Florin Boca, University of Illinois at Urbana-Champaign
Title:Farey statistics and the distribution of eigenvalues in large sieve matrices
Abstract:Some parts of the fine distribution of Farey fractions (a.k.a. roots of unity) is captured by their spacing statistics (consecutive gaps and correlations). A large sieve matrix is a N x N matrix A*A, where A is a Vandermonde type matrix defined by roots of unity of order at most Q. The classical large sieve inequality provides an upper bound estimate for the largest eigenvalue of A*A. This talk will discuss some connections between these topics. We will focus on the behavior of these matrices when N ~ cQ^2, with Q --> infty and c>0 constant, establishing asymptotic formulas for their moments and proving the existence of a limiting distribution for their eigenvalues as a function of c. This is joint work with Maksym Radziwill.

Date:November 17, 2017
Time:4:00pm
Location:BLOC 220
Speaker:Anna Skripka, University of New Mexico
Title:Schur multipliers in perturbation theory.
Abstract:Schur multipliers and their generalizations have been actively studied for over a century. Classical linear Schur multipliers act on matrices as entrywise multiplications; multilinear Schur multipliers act by some intricate products. After recalling finite dimensional Schur multipliers, we will concentrate on their generalizations to multilinear transformations arising in infinite dimensional perturbation theory and consider an application to approximation of operator functions. In particular, we will discuss sharp conditions for Schatten class membership of remainders of approximations [1]. The affirmative case relies on the approach to Schur multipliers without separation of variables emerging from [3] and addressed in the nonself-adjoint case in [2]. [1] "Multilinear Schur multipliers and applications to operator Taylor remainders", with D. Potapov, F. Sukochev, and A. Tomskova, Adv. Math., 320 (2017), 1063-1098. [2] "Estimates and trace formulas for unitary and resolvent comparable perturbations", Adv. Math., 311 (2017), 481-509. [3] "Spectral shift function of higher order", with D. Potapov and F. Sukochev, Invent. Math., 193 (2013), no. 3, 501-538.

Date:December 1, 2017
Time:4:00pm
Location:BLOC 220
Speaker:Li Gao, University of Illinois at Urbana-Champaign
Title:Entropic uncertainty relations via Noncommutative Lp Spaces
Abstract:The Heisenberg uncertainty principle states that it is impossible to prepare a quantum particle for which both position and momentum are sharply defined. Entropy is a natural measure of uncertainty. The first entropic formulation of the uncertainty principle was proved by Hirschman and since then entropic uncertainty relations have been obtained for many different scenarios, including some recent advances on uncertainty relations with quantum memory. In this talk, I will present an approach to entropic uncertainty relations via noncommutative Lp norms. We show that the natural connection between noncommutative Lp Spaces and Renyi information measure gives certain uncertainty relation for two complementary subalgebras of a tracial von Neumann algebra. This is a joint work with Marius Junge and Nicholas LaRacuente.