Events for 04/18/2024 from all calendars

Working Seminar on Banach and Metric Spaces

Time: 10:00AM - 11:30AM

Location: BLOC 302

Speaker: Hung Viet Chu, Texas A&M University

Title: The Radon-Nikodym property and curves with zero derivatives for nonlocally convex spaces (after Nigel Kalton)

Noncommutative Geometry Seminar

Time: 3:00PM - 4:00PM

Location: BLOC 628

Speaker: Qiaochu Ma, Washington University in St. Louis

Title: Mixed quantization and quantum ergodicity

Abstract: Quantum Ergodicity (QE) is a classical topic in spectral geometry and quantum chaos, it states that on a compact Riemannian manifold whose geodesic flow is ergodic with respect to the Liouville measure, the Laplacian has a density-one subsequence of eigenfunctions that tends to be equidistributed. In this talk, we present a uniform version of QE for a certain series of unitary flat bundles using a mixture of semiclassical and geometric quantizations. We shall see that even if analytically unitary flat bundles are similar to the trivial bundle, the holonomy provides extra fascinating geometrical phenomena.

Departmental Colloquia

Time: 4:00PM - 5:00PM

Location: BLOC 302

Speaker: Henri Moscovici

Title: Can one hear the zeros of zeta?

Abstract: Preceding by a half-century the well-known challenge “Can one hear the shape of a drum?” a similar dare was raised relative to the Riemann Hypothesis, which in contemporary parlance goes by the name of “Hilbert-Polya operator”. Very recently Alain Connes worked out the heat expansion for such an operator, assuming its existence. After presenting his results I will discuss the connection with our joint work on the square-root of the prolate spheroidal wave operator, whose spectrum simulates the zeros of Zeta.

Can one hear the zeros of zeta?

Time: 4:00PM - 5:00PM

Location: BLOC 302

Speaker: Henri Moscovici

Description: Preceding by a half-century the well-known challenge “Can one hear the shape of a drum?” a similar dare was raised relative to the Riemann Hypothesis, which in contemporary parlance goes by the name of “Hilbert-Polya operator”. Very recently Alain Connes worked out the heat expansion for such an operator, assuming its existence. After presenting his results I will discuss the connection with our joint work on the square-root of the prolate spheroidal wave operator, whose spectrum simulates the zeros of Zeta.

AMUSE

Time: 6:00PM - 7:00PM

Location: BLOC 306

Speaker: Dr. William Rundell, Texas A&M University, Mathematics

Title: Eigenvalues; matrices and into differential equations: Can you hear the density of a vibrating string or the shape of a drum?

Abstract: In an undergraduate curriculum one sees eigenvalues in linear algebra and in the basic o.d.e. class one writes systems of equations, converts to a matrix question, and interprets the eigenvalues as pointers to the system's behaviour. We will go over this briefly enough to see the pattern of: "have problem, find eigenvalues, interpret behaviour." But it is a more interesting question to turn this around: "I have a differential equation or a system of such and its eigenvalues are known; what can you say about the system?" This is a partial explanation for the cryptic title. The purpose of the talk is to fill in some of the reasoning (and of course answer the questions in the title).