Events for 01/28/2021 from all calendars

Mathematical Physics and Harmonic Analysis Seminar

Time: 11:00AM - 11:50PM

Location: Zoom

Speaker: Ralph Kaufmann, Purdue University

Title: Local Models and Global Constraints

Abstract: Motivated by current research in condensed matter, we consider multi-parameter families of Hamiltonians which may have multiple Eigenvalues at so-called critical points. In this setting, we address several questions. In particular, for 3-d families with isolated critical points, we can give classification theorems for the local structures. We also show more generally that one can associate topological invariants to such systems, by various methods such as Chern classes and slicing. Finally, we investigate global constraints on the local structures and give theorems for the case in which the parameter space is a three-torus, which is relevant to real world periodic systems. We illustrate these constraints on a concrete system, the Gyroid, and its deformations.