Institut für Analysis

Forschungsrichtungen am Institut für Analysis

Global Analysis

  • Elliptic and parabolic PDEs on manifolds with geometric singularities
  • Spectral geometry on manifolds
  • Index theory of elliptic and non-elliptic differential operators
  • Scattering theory on manifolds
  • Harmonic Analysis

Mathematical Physics

  • Operators on quantum graphs
  • Quantum field theory on curved spacetimes
  • Geometric quantisation and deformation quantisation
  • Quantisation of gravity coupled to matter
  • Spectral theory with magnetic fields
  • Mathematical theory of Casimir interactions

Operator Algebras

  • K-theory of operator algebras and index theory.
  • Algebras of pseudo-differential operators and boundary value problems
  • Constructive approaches to spectral triples

Partial Differential Equations

  • Spectral theory for differential operators
  • Dispersive estimates and control theory
  • Microlocal analysis and semi-classical analysis