My main mathematical interests concern Mathematical Physics, specifically "Hydrodynamic Limits", i.e. the macroscopic derivation of fluid equations from a microscopic point of view. One reason for wanting to do so is to achieve a microscopic understanding of the Laws of Thermodynamics, which are otherwise either taken as given or as experimental evidences.
Besides the physical motivation, Hydrodynamic Limits offer a wide range of challenges that span from Probability Theory to Analysis of Nonlinear PDEs. One may in fact aim to use Hydrodynamic Limits as a tool to solve open problem in such other branches of Mathematics.