Ursula Ludwig Home Page
The main focus of my research lies in the interaction of geometry, topology and analysis on singular spaces. Singular spaces arrive naturally in geometry, the most prominent examples being quotients of manifolds under group actions, or - in algebraic geometry - zero sets of polynomia.
I have studied singular spaces from different viewpoints: After my DEA and Diploma-thesis in algebraic geometry, I switched for my PhD project to studying singular spaces with methods from differential topology, differential geometry and dynamical systems.
In the last few years I started to use intersection homology tools on singular spaces on the one hand and analytic techniques (L2-techniques) as well as methods from global analysis on the other.
In particular I worked successfully on the generalisation of the Witten deformation and the Cheeger-Müler Theorem to singular spaces.
- topological and analytic invariants of singular spaces
- (stratified) Morse-Novikov theory
- Witten deformation
- global analysis, index theory, analytic and topological torsion