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.