Analysis, Geometric Structures and Mathematical Physics

The members of this research focus area study a broad range of topics. There are strong ties between these topics, for example via methods of functional analysis and the theory of differential equations, which are applied to questions of complex analysis, differential geometry, and mathematical physics. Functional analysis and differential equations provide connections to other research focus areas of the faculty of mathematics, in particular to the focus area "computational sciences". 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 focus group have stong connections to physics (general relativity). 

Main topics of research in the focus area

  • 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.
  • Mathematical physics: Spectral theory and integrable wave equations; modelling of water waves; 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

DIANA (Differential Algebras and Nonlinear Analysis)

Differentialgeometrie

Komplexe Analysis

Mathematische Physik und Partielle Differentialgleichungen