Forschungsrichtungen am Institut für Analysis

Singular Analysis

Elliptic and parabolic PDE on Manifolds with geometric singularities such as cusps, cones and edges

Spectral geometry


Quantisation of gravity coupled to matter via Ashtekar-Barbero-Sen variables and noncommutative geometry
Geometric quantisation
Deformation quantisation

Noncommutative Geometry and Operator Algebras

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

Spectral Theory

Spectral theory with magnetic fields.
Operators on metric graphs (quantum graphs).