Research interests

  • applied mathematics, partial differential equations (parabolic, hyperbolic, Schrödinger-type)
  • large- & short-time behavior of evolution equations (PDEs, operator equations, ODEs): entropy methods, hypocoercivity, degeneracies, limiting amplitude principle for wave equations;
  • (quantum) kinetic equations: well-posedness, stability, pseudo-differential Wigner models;
  • functional inequalities: log Sobolev-,  generalized Poincaré- & Csiszár-Kullback-type;
  • structure preserving schemes: Schrödinger & Dirac-type equations, discrete open boundary conditions, discrete analoga of hypocoercive evolutions;
  • efficient numerical methods for highly oscillatory problems (Schrödinger, wave equations): WKB-based schemes, semi-classical limit, adaptivity;
  • applications: quantum transport (nano devices, open quantum systems), mechanical control systems, underwater acoustics, molecular dynamics simulation of liquid germanium.

Recent Talks