The Landscape Law and Wave Localization

Explore the intricacies of wave localization and the landscape law in this illuminating talk by Svitlana Mayboroda from the University of Minnesota. Delivered as part of the inaugural ZhengTong Chern-Weil Symposium in Mathematics at the University of Chicago, the one-hour presentation titled "The Landscape Law and Wave Localization" delves into the phenomenon of wave confinement in complex systems. Discover how the landscape function can predict the behavior of localized eigenfunctions, their exponential decay patterns, and provide accurate eigenvalue bounds. Learn about groundbreaking non-asymptotic estimates on the integrated density of states for the Schrödinger operator, utilizing a counting function for localization landscape minima. Gain insights into how geometric complexity and potential randomness influence wave behavior in various systems.