# Events for April 21, 2017 from General and Seminar calendars

## Probability Seminar

Time: 1:50PM - 2:50PM

Location: BLOC 628

Speaker: Shahaf Nitzan

Title: Persistence as a spectral property

Abstract: A Gaussian stationary process is a random function f: Z --> R, or f: R --> R, for which any vector (f(x_1), ..., f(x_n)) has a centered multi-normal distribution and whose distribution is invariant to shifts. Persistence is the event of such a random function to remain positive on a long interval [0,N]. Estimating the probability of this event has important implications in engineering , physics, and probability. However, though active efforts to understand persistence were made in the last 50 years, until recently, only specific examples and very general bounds were obtained. In the last few years, a new point of view simplifies the study of persistence, namely - relating it to the spectral measure of the process. In this talk we will use this point of view to study the persistence in cases where the spectral measure is 'small' or 'big' near zero. This talk is based on Joint work with Naomi Feldheim and Ohad Feldheim.

## Mathematical Physics and Harmonic Analysis Seminar

Time: 1:50PM - 2:50PM

Location: BLOC 628

Speaker: Shahaf Nitzan, Georgia Tech

Title: Persistence as a spectral property

Abstract: A Gaussian stationary process is a random function f: Z --> R, or f: R --> R, for which any vector (f(x_1), ..., f(x_n)) has a centered multi-normal distribution and whose distribution is invariant to shifts. Persistence is the event of such a random function to remain positive on a long interval [0,N]. Estimating the probability of this event has important implications in engineering , physics, and probability. However, though active efforts to understand persistence were made in the last 50 years, until recently, only specific examples and very general bounds were obtained. In the last few years, a new point of view simplifies the study of persistence, namely - relating it to the spectral measure of the process. In this talk we will use this point of view to study the persistence in cases where the spectral measure is 'small' or 'big' near zero. This talk is based on Joint work with Naomi Feldheim and Ohad Feldheim.

## Algebra and Combinatorics Seminar

Time: 3:00PM - 3:50PM

Speaker: TAGS, Rice University

Title: Texas Algebraic Geometry Symposium

## Banach Spaces Seminar

Time: 3:00PM - 4:00PM

Location: BLOC 220

Speaker: Florence Lancien, Université de Franche-Comté

Title: Discrete analyticity for vector valued convolutions

Abstract: In 1986 G. Pisier showed that some convolution semigroups of operators are analytic bounded on Lp(X) for 1<p<∞ iff X is a K-convex Banach space. The analogue of analyticity for discrete semigroups is the notion of Ritt operators: T∈B(X) s.t. supn‖Tn(I-T)‖<∞. We show that Pisier's theorem adapts to this situation and explain how this is related to the question of subordination for discrete semigroups.This is joint work with C. Le Merdy

## Linear Analysis Seminar

Time: 4:00PM - 5:00PM

Location: BLOC 220

Speaker: Michael Brannan, TAMU

Title: Quantum Cayley trees and the structure of orthogonal free quantum group factors

Abstract: In this talk I will survey some recent results on the structural theory of a class of II_1-factors arising from a family of discrete quantum groups, called the orthogonal free quantum groups FO_n. A question that has been around for some time is whether or not an orthogonal free quantum group factor L(FO_n) can be isomorphic to a free group factor L(F_k). We answer this question in the negative by proving that L(FO_n) is a strongly 1-bounded von Neumann algebra in the sense of Kenley Jung. We obtain this result by proving a certain spectral regularity result for the edge reversing operator on the quantum Cayley tree of FO_n and connect this result to a recent free entropy dimension result of Jung and Shlyakhtenko. This is joint work with Roland Vergnioux.

## Geometry Seminar

Time: 10:00PM - 6:00PM

Speaker: TAGS Conference