Large-Scale Geometry Obstructs Localization
Time: 2022-10-07
Published By: Wenqiong Li
Speaker(s): Guo Chuan Thiang (BICMR)
Time: 14:00-15:00 October 11, 2022
Venue: Room 29, Quan Zhai, BICMR
Given a spectral subspace of a self-adjoint geometric operator, is it possible to find some orthonormal basis of exponentially-localized functions, centered on some uniformly discrete lattice of the manifold? M. Ludewig and I proved that large-scale geometry induces a coarse K-theory index obstruction to this wishful thinking. Informally, certain Hilbert subspaces are fundamentally delocalized, and cannot admit lattice approximations. This “macroscopic anomaly” is characteristic of topological phases of matter.
