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).