Probabilistic aspects of geometric evolution equations.

Seminar in Mathematics

Abstract: The main topic of this talk is the construction of Gibbs measures and the study of their invariance for geometric evolution equations. To make this accessible, we first discuss invariant Gibbs measures for finite-dimensional Hamiltonian and Langevin equations on manifolds. We then consider Gibbs measures in the context of the wave maps equation and the stochastic Yang–Mills–Higgs equation, two important examples of geometric evolution equations. For both models, the well-posedness theory relies on an intricate combination of analytic, geometric, and probabilistic techniques.