Speaker: Guo Chuan Thiang ，Peking University

Inviter: 王晋民副研究员

Title: Large-scale geometry obstructs localization

Language: Chinese

Time & Venue: 2024.10.22 10:30-11:30 晨兴410

Abstract: Given a Riemannian manifold, we may choose a discretization and find a localized basis for the Hilbert space of square-integrable functions. However, there exist natural Hilbert subspaces which do not admit such a discretely-localized description. This is based on the concept of topological insulators in physics, as quantum systems with no atomic limit. I will explain that the obstruction to localizing a Hilbert subspace is a coarse-geometric invariant, which can be computed by an index formula with concrete physical meaning. The lesson is that discretization of space has a very different meaning in quantum mechanics, with invariants going beyond the classical topological ones associated to triangulations of the manifold.