The APDE seminar on Monday, 9/29, will be given by Andrea Nahmod (UMass Amherst) in-person in Evans 736, and will also be broadcasted online via Zoom from 4:10pm to 5:00pm PDT. To participate, please email Adam Black (adamblack@berkeley.edu).

Title: Probabilistic scaling, propagation of randomness and invariant Gibbs measures

Abstract: In this talk, we will start by describing how classical tools from probability
offer a robust framework to understand the dynamics of waves via appropriate ensembles
on phase space rather than particular microscopic dynamical trajectories. We will continue
by explaining the fundamental shift in paradigm that arises from the “correct” scaling in this
context and how it opened the door to unveil the random structures of nonlinear waves that
live on high frequencies and fine scales as they propagate. We will then discuss how these
ideas broke the logjam in the study of the Gibbs measures associated to nonlinear
Schrödinger equations in the context of equilibrium statistical mechanics and of the
hyperbolic Phi^4_3 model in the context of constructive quantum field theory.
We will end with some open challenges about the long-time propagation of randomness
and out-of-equilibrium dynamics.

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.