Large-Scale Geometry Obstructs Localization
发布时间：2022年10月07日
浏览次数：2435
发布者: Wenqiong Li
主讲人： 程国传（北京国际数学研究中心）
活动时间： 从 2022-10-11 14:00 到 15:00
场地： 北京国际数学研究中心，全斋全29教室
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.
