The APDE seminar on Monday, 9/22, will be given by Adam Black (UC Berkeley) in-person in Evans 736, and will also be broadcasted online via Zoom from 4:10pm to 5:00pm PDT. To participate, please email Ryan Unger (runger@berkeley.edu).

Title: Quantum diffusion and random matrix theory

Abstract: The Schrödinger equation with a random potential serves as a simple model for the propagation of waves in a disordered medium. It is conjectured that when the strength of the potential is weak, the solution should evolve diffusively as time goes to infinity. In this talk, I will explain a new proof of this phenomenon for long but finite times. The proof combines ideas from random matrix theory with resolvent estimates for the Laplacian. This is joint work with Reuben Drogin and Felipe Hernández.