My research is in geometric analysis, that is, 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.
Topics I am interested in include:
- Einstein equations (vacuum and coupled to fluids, electromagnetism)
- singularities in general relativity (black holes and naked singularities)
- global and asymptotic behavior of solutions
- nonlinear wave equations and hyperbolic conservation laws
- weak Riemannian and Lorentzian geometry (including metric geometry)
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 based upon my work.