Events for 03/03/2017 from all calendars

Mathematical Physics and Harmonic Analysis Seminar

Time: 1:50PM - 2:50PM

Location: BLOC 628

Speaker: Jeffrey Galkowski, McGill University

Title: Scarring and L^\infty norms of Eigenfunctions

Abstract: We study the relationship between L^\infty growth of eigenfunctions and their L^2 concentration as measured by defect measures. In particular, we show that scarring in the sense of concentration of defect measure on certain submanifolds is incompatible with maximal L^\infty growth. In addition, we show that a defect measure which is too diffuse, such as the Liouville measure, is incompatible with maximal eigenfunction growth. 

Seminar on Banach and Metric Space Geometry

Time: 3:00PM - 4:00PM

Location: BLOC 220

Speaker: Beatrice-Helen Vritsiou, University of Michigan

Title: Selberg-type integrals and the variance conjecture for the operator norm

Abstract: We will discuss the variance conjecture from Asymptotic Convex Geometry in the case of unit balls of the p-Schatten norms in different classical subspaces of square matrices (e.g. the subspaces of symmetric or Hermitian matrices). In particular, we will show how to resolve the conjecture for the unit ball of the operator norm in all these subspaces (this improves upon previous joint work with J. Radke). By Random Matrix Theory results, the question in such cases can be reduced to estimation of integrals of highly symmetric distributions, which may be more amenable to analytic or combinatorial techniques. In the case of the operator norm, integrals of the corresponding symmetric distributions (at least some specific instances of them) have been analysed by Selberg and others, and we manage to use the nice expressions they have found for them.

Algebra and Combinatorics Seminar

Time: 3:00PM - 3:50PM

Location: BLOC 628

Speaker: Yuyu Zhu, Texas A&M University

Title: A Fast Algoritm for Complex Feasibility

Abstract: Complex feasibility is the problem of deciding if a system of polynomials with integer coefficients has a complex solution. Koiran proved that under the assumption of generalized Riemann Hypothesis, this problem is in the polynomial hierarchy. We will talk about a fast algorithm to determine the satisfiability of the system based on this result. We will also look for weaker assumptions aided with results and conjectures on prime density.

Linear Analysis Seminar

Time: 4:00PM - 5:00PM

Location: BLOC 220

Speaker: Ken Dykema, Texas A&M University

Title: Commuting operators in finite von Neumann algebras

Abstract: We find a joint spectral distribution measure for families of commuting elements of a finite von Neumann algebra. This generalizes the Brown measure for single operators. Furthermore, we find a lattice (based on Borel sets) consisting of hyperinvariant projections that decompose the spectral distribution measure. This leads to simultaneous upper triangularization results for commuting operators and behaves well with multivariate holomorphic functional calculus. (Joint work with Ian Charlesworth, Fedor Sukochev and Dmitriy Zanin.)