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Texas A&M University
Mathematics

Events for 10/21/2020 from all calendars

Noncommutative Geometry Seminar

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Time: 1:00PM - 2:00PM

Location: Zoom 942810031

Speaker: Jonathan Block, University of Pennsylvania

Title: Singular foliations and characteristic classes

Abstract: We revisit the residue theorem of Baum and Bott computing characteristic classes for certain objects in terms of residues calculated along the singularities of a foliation using techniques from higher homotopy structures.

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Probability Seminar

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Time: 2:00PM - 3:00PM

Location: Zoom

Speaker: Phanuel Mariano, Union College

Title: Can you hear the fundamental frequency of a drum using probability?

Abstract: In Mark Kac's famous 1966 paper, he asked "Can you hear the shape of a drum?" The precise question being, if you heard the full list of overtones and frequencies while you were blindfolded, would you be able to tell the shape of the drumhead $D\subset\mathbb{R}^2$ in some mathematical way? The problem I will primarily speak about is in regards to how the fundamental frequency of a drum and probability theory are related. This connection will be through an inequality involving the fundamental frequency of a drum with drumhead $D\subset\mathbb{R}^d$ and the maximum expected lifetime of Brownian motion started inside a domain $D\subset\mathbb{R}^d$. We improve on the constants of a known inequality and prove a new asymptotically sharp inequality involving the moments of the expected lifetime of Brownian motion. We discuss conjectures about the sharp inequality and present our partial results about the extremal domains and sharp constants over a nice class of domains. This talk is based on joint work with Rodrigo Bañuelos and Jing Wang.


Topology Seminar

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Time: 4:00PM - 5:00PM

Location: Zoom

Speaker: Sara Maloni, University of Virginia

Title: Convex hulls of quasicircles in hyperbolic and anti-de Sitter space.

Abstract: Thurston conjectured that quasi-Fuchsian manifolds are determined by the induced hyperbolic metrics on the boundary of their convex core and Mess generalized those conjectures to the context of globally hyperbolic AdS spacetimes. In this talk I will discuss a universal version of these conjectures (and prove the existence part) by considering convex sets spanning quasicircles in the boundary at infinity of hyperbolic and anti-de Sitter space. This work generalizes Alexandrov and Pogorelov's results about the characterization metrics induced on the boundary of a compact convex subset of hyperbolic space. Time permitting, we will discuss why in hyperbolic space quasicircles can't be characterized by the width of their convex hulls, except when the convex hulls have small width. This is different than the anti-de Sitter setting, as Bonsante and Schlenker showed. (This is joint work with Bonsante, Danciger and Schlenker.)