Max Planck Institute for Mathematics in the Sciences, Leipzig Universität Bielefeld, Fakultät für Mathematik
@ Germany.
Benjamin is a reseach group leader at the MaxPlanck Institute for Mathematics in the Sciences.
Their research centers around stochastic partial differential equations (SPDE), random dynamical systems, rough paths, stochastic scalar conservation laws and singulardegenerate quasilinear SPDE, with emphasis on stochastic porous media equations, stochastic fast diffusion equations and pLaplace equations.

Large deviations for conservative, stochastic PDE and nonequilibrium fluctuations
Macroscopic fluctuation theory provides a general framework for far from equilibrium thermodynamics, based on a fundamental formula for large fluctuaWons around (local) equilibria. This fundamental postulate can be informally justified from the framework of fluctuating hydrodynamics, linking far from equilibrium behavior to zeronoise large deviaWons in conservative, stochastic PDE. In this talk, we will give rigorous justification to this relation in the special case of the zero range process. More precisely, we show that the rate funcWon describing its large fluctuations is identical to the rate function appearing in zero noise large deviations to conservative stochastic PDE, by means of proving the Gammaconvergence of rate functions to approximating stochastic PDE. The proof of Gammaconvergence is based on the wellposedness of the skeleton equation  a degenerate parabolichyperbolic PDE with irregular coefficients, the proof of which extends DiPernaLions' renormalization techniques to nonlinear PDE.
