I am interested in analysis and differential geometry, and the interplay between both fields. I apply techniques from analysis, in particular partial differential equations, to problems in (semi-)Riemannian geometry and mathematical general relativity. The enveloping field of my research is geometric analysis.
Topics I am interested in include:
- Einstein equations (vacuum and coupled with perfect fluids)
- nonlinear wave equations in general
- global and asymptotic behavior of solutions
- formation of singularities (in particular, black holes)
- weak semi-Riemannian geometry
- and related topics
Apart from pure mathematics I am also interested in mathematical problems arising in geosciences.
For a generally understandable description of my work you are invited to read some press articles (in German) based upon my work.