University of Washington, Department of Mathematics.
September 19, 2024 in CMU 226.
Schedule:
All talks will be held at CMU 226.
Welcome address at 9:45 am.
10 am -- 10:45 am - Soumik Pal speaks on the contributions of Chris Burdzy
10:55 am -- 11:40 am - Steffen Rohde speaks on the contributions of Don Marshall
11:50 am -- 12:35 pm - Gabriel Paternain speaks on the contributions of Gunther Uhlmann
Lunch break from 12:35 pm till 2:20 pm
2:20 pm – 2:50 pm: Talk by Alexis Drouot
3:00 – 3:30 pm: Talk by Dima Drusvyatsky
3:40 – 4:10 pm: Talk by Bobby Wilson
4:20 – 4:50 pm: Talk by Jon Zhu
Concludes at 5 pm.
Dinner at 5:30 p.m. at Piatti, U-Village
Organizers: Alexis Drouot, Soumik Pal and Steffen Rohde
Alexis Drouot
Mathematical results on topological insulators.
Topological insulators are striking quantum materials which block electricity in their interior but support robust currents along their boundary. The bulk-edge correspondence is a physical principle that expresses the conductance of the boundary in terms of a bulk topological invariant. We will give a state-of-the-art review of the subject, including recent results in collaboration with our postdoc Xiaowen Zhu.
Dima Drusvyatsky
Sensitivity, robustness, and numerical efficiency in computational mathematics and statistics.
A central theme in computational mathematics is that the numerical difficulty of solving a given problem is closely related to both (i) the sensitivity of its solution to perturbations and (ii) the shortest distance of the problem to an ill-posed instance. In this talk, I will survey surprisingly tight estimates relating these three seemingly distinct notions for high-profile problems in convex optimization and statistical estimation. In the process, we will encounter a blend of techniques from optimization, nonsmooth analysis, and optimal transport. The talk is meant to be broadly accessible and no background, aside from basic linear algebra, will be assumed.
Bobby Wilson
Falconer's Distance Set Problem in General Geometries
We will discuss the problem of estimating the minimal size of a set of distances determined by a given set of points. The analyst's version of the problem has garnered a lot of interest, and is typically examined using restriction estimates. We will present the basics of the problem, how the Fourier-analytic estimates are used to make progress on the main conjecture, and new algorithmic techniques that are being developed to approach the problem.
Jonathan Zhu
Complexity estimates for surfaces
There are various natural geometric quantities which capture the content or complexity of an object, such as the minimax width of a manifold or the (Gaussian) area of a surface. Extremal objects for these quantities are important topics of study. We’ll focus on the use of techniques from minimal surface theory, but also discuss potential connections to probability.