Deterministic Localization for the Discrete Schrodinger Operator

Explore a mathematics department colloquium talk where Artur Avila from the University of Zurich presents his research on deterministic localization for discrete Schrodinger operators. Learn how discrete Schrodinger operators with bounded potentials on large finite boxes N^d can have most eigenfunctions delocalized with uniformly small deterministic perturbation of the potential. The presentation explains how this result derives from a dynamical result about ergodic Schrodinger operators on Z^d through a correspondence principle in Furstenberg's spirit. Discover the optimization technique underlying the proof, which utilizes a "Hellman-Feynman formula" for the integrated density of states. This 72-minute talk represents joint work with David Damanik and was presented at Stony Brook Mathematics on April 28, 2025.