Jacob Shapiro – Princeton University
Wednesday, August 20th, 2025
Zoom opens: 10:30AM DST
Seminar begins: 10:45AM DST
Classification of spectrally-gapped non-interacting insulators
Topological insulators exhibit observables that are quantized and experimentally stable. Classifying these systems is usually done via standard tools in algebraic topology (chiefly K-theory), but such an analysis focuses more on quantization and less on experimental stability. Moreover, treating systems with Anderson localization or interactions poses challenges in such standard frameworks, which motivates exploring other tools to tackle this question. We propose a purely functional analytic perspective that calculates the set of path-components of insulators directly. Our perspective is characterized by introducing two new notions: (1) spherical-locality and (2) bulk-non-triviality. I will explain the resolution of this problem in 1D and report on progress in higher dimensions. This talk is based on joint work with Jui-Hui Chung.