Analysis, Geometric Structures and Mathematical Physics

The members of this Key Research Area study a wide range of topics, which possess strong ties between each other, for example via methods of functional analysis and the theory of differential equations, which are applied to questions of complex analysis, differential geometry, low dimensional topology, and mathematical physics. Functional analysis and differential equations provide connections to other Key Research Area of the Faculty of Mathematics, in particular to the Key Research Area "Computational Sciences''. Algebraic geometry, Lie theory, representation theory and topological quantum field theory lead to natural connections to the area "Algebra, Number Theory and Discrete Mathematics". Apart from mathematical physics, also many of the geometric topics studied by members of this Key Research Area have stong connections to physics (general relativity). 

Main topics of research in the focus area

  • Algebraic geometry: moduli spaces, enumerative geometry.
  • Complex analysis: Spaces of holomorphic functions in several variables; CR-geometry.
  • Differential geometry: infinite-dimensional differential geometry; geometric structures and applications of representation theory, parabolic geometries; Riemannian geometry, minimal surfaces, CMC surfaces, and geometric analysis.
  • Low dimensional topology: contact structures, Heegaard Floer invariants, knots and TQFTs.
  • Mathematical physics: Spectral theory and integrable wave equations; modelling of water waves;  nonlinear dispersive partial differential equations; conformal and topological quantum field theory, knot invariants; general relativity.
  • Nonlinear functional analysis: calculus in inifinite dimensional spaces; nonlinear theory of generalized functions.

Research groups and members

Algebraic geometry

Complex analysis

Differential geometry

Mathematical physics and partial differential equations

Low dimensional Topology