My research interests
- nonlinear Schrödinger equations
- high frequency asymtotics: WKB methods and Wigner functions,
- Gross-Pitaevskii equation,
- electron dynamics in crystals and nanostructures,
- nonlinear wave propagation,
- dispersion estimates,
- spectral-time splitting discretisations.
- classical and quantum kinetic equations
- entropy dissipation techniques and convex Sobolev inequalities,
- simulations of Bose-Einstein condensates,
- quantum scattering in semiconductors: Boltzmann equation,
- collective behaviour of swimming mirco-organismns and chemotaxis,
- kinetics and mean field models for human crowding behaviour, Pareto economics and opinion formation in human societies,
- mean-field limits.
- reaction-diffusion/convection systems
- drift and diffusion of charge carries in semiconductors,
- large-time asymptotics
- finte element discretisations.
People I collaborate with