Peter Markowich

  • Department of Applied Mathematics and Theoretical Physics

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

I’m currently working on 1 CCIMI project

Formation and Adaption of Biological Transportation Networks

View the project

Key Publications