Research interests: hinetic equations, Hyperbolic systems, Boltzmann equations, hydrodynamic limits, damped-driven chaotic and stochastic systems, numerical schemes for PDEs
Much of my research has revolved around the central theme of understanding how large-scale behaviors emerge from dynamics or structures on small-scales. This includes the classical question of statistical physics about the macroscpic desciption of systems of large numbers of particles given known microscopic physics. It also includes studies of semiclassical limits of nonlinear wave equations, convergence of numerical schemes, turbulence modeling, derivations of shallow water systems, derivations of fluid dynamical systems from kinetic theories, radiation transport through random media, and many other areas. These problems all fall into the what is now called the class of "multiscale" problems.