Welcome to the website of researchers working in Bilbao (either at UPV/EHU or at BCAM) in mathematical analysis, partial differential equations, inverse problems, mathematical physics, and/or related topics.
BCAM, Tuesday, June 16th, 2026, 17:00 - 18:00
Invariant Gibbs measures and propagation of randomness for nonlinear dispersive and wave PDE.
Andrea Nahmod - UMass Amherst
In this talk, we will review recent joint works with Yu Deng and Haitian Yue on the solution of the invariance of the Gibbs measure under the 2D nonlinear Schrödinger flow (NLS) flow and of the 3D cubic nonlinear wave equation (NLW) with Bringmann, Deng and Yue. In particular, we will discuss the method of random averaging operators and the development of the random tensors theory. The latter yielded the resolution of the random data Cauchy problem for NLS in its full probabilistic subcritical regime. Along the way we will explain the fundamental shift in paradigm that arises from the notion of probabilistic scaling for random data Cauchy problems and how these ideas opened the door to unveil the random structures of nonlinear waves that live on high frequencies and fine scales as they propagate. We will end the talk with a short discussion of some current open challenges.