Wave Localization and the Landscape Law

Explore the fascinating world of wave localization and the landscape law in this 57-minute webinar from SIAM's Seminar in the Analysis and Methods of PDE. Delve into the ubiquitous presence of waves across electromagnetic, acoustic, and quantum mechanical realms as Svitlana Mayboroda from ETH Zürich presents recent advancements in manipulating individual atoms. Discover the concept of a landscape behind disordered systems and its ability to predict localized eigenfunctions, exponential decay patterns, and eigenvalue bounds. Learn about the first non-asymptotic estimates on the integrated density of states of the Schrödinger operator and initial results in predicting Wigner functions and quantum observables. Gain insights into the challenges of understanding waves in complex or random media and the fascinating behavior of localization. The webinar concludes with a Q&A session, offering an opportunity to further explore this cutting-edge research in wave dynamics and partial differential equations.