Applied Math Seminar

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Constructing optimal Wannier functions via potential theory

Speaker: Hanwen Zhang, Yale

Location: Warren Weaver Hall 1302

Date: Friday, November 14, 2025, 2:30 p.m.

Synopsis:

Wannier functions provide localized real-space representations of electronic and photonic states in periodic media, forming the mathematical bridge between band theory and lattice models. Yet constructing the most localized Wannier functions has long relied on heuristic gauge choices and high-dimensional optimization. In this talk, I will describe an analytic framework that corrects Kato’s classical perturbation theory on tori by incorporating geometric quantities such as the Berry connection and curvature, thereby turning a local analytic theory into a global one. This yields a constructive procedure for efficiently computing optimally localized Wannier functions and reveals a unified link among localization, geometry, and topological obstruction. The framework will be illustrated with several numerical examples.