•   mathematical fluid mechanics

•   compressible gas dynamics, magnetohydrodynamics

•   kinetic modeling, kinetic modeling of gas mixtures and of plasma, numerics for this

•   theory of hyperbolic conservation laws: well-posedness in one and multiple space dimensions, relaxation limits, discontinuous flux conservation laws

•   modeling macroscopic fluid flow equations via microscopic interacting particle systems

•   numerics for hyperbolic conservation laws: finite volume schemes in one and multiple space dimensions, approximate Riemann solvers, discontinuous Galerkin methods, moving mesh methods

•   low Mach limits for the Euler equations and equations of ideal magnetohydrodynamics, also with gravity, both theoretical and numerical

•   well-balanced schemes applied to the Euler equations and equations of ideal magnetohydrodynamics, both with gravity

•   numerical methods that preserve stationary solutions for for kinetic and fluid equations

•  uncertainty quantification, theoretical coercivity estimates, numerical simulations for kinetic and fluid equations

•   astrophysical applications: accretion discs, protostellar jets, turbulence modeling, large eddy simulations, star formation, stellar evolution, galaxy evolution