I work at the meeting point of nonlinear partial differential equations and stochastic analysis. Most of my research asks a single question in different guises: what does a Hamiltonian or fluid equation preserve over long times, and what can a well-chosen measure tell us that a single trajectory cannot?

That question has taken me through invariant measures for the Benjamin–Ono and Klein–Gordon equations, almost sure global well-posedness in the energy supercritical regime, with applications to the nonlinear Schrödinger equations, and invariant measures for the surface quasi-geostrophic and Euler equations. The method built on inviscid limits of damped and driven equations, turns out to reach problems where deterministic techniques stop.

Since taking the German Research Chair at AIMS Rwanda I have been building something alongside the research: a school focused on probabilistic methods in PDEs, within a DAAD cooperation with Bielefeld University.