Research interests
I am interested in the interplay between analysis, geometry and physics. Broadly speaking one could classify my research as geometric analysis and mathematical physics. I develop and apply techniques from analysis, including partial differential equations, and metric geometry to problems in (semi-)Riemannian geometry and mathematical general relativity.
Topics I am interested in include:
- mathematical general relativity
- Einstein equations (vacuum and with matter, in particular, fluids and electromagnetism)
- black holes and naked singularities
- global and asymptotic behavior of solutions
- global Riemannian and Lorentzian geometry (including metric geometry)
- synthetic and analytic approaches for nonsmooth spaces and spacetimes
- causality theory
- analysis and geometry of metric (measure) spaces
- nonlinear wave equations and hyperbolic conservation laws
Apart from pure mathematics and mathematical physics I am also interested in mathematical problems arising in geosciences.
See also
List of Publications
Conferences, Talks, Research stays etc.
Grants and Awards
For a generally understandable description of my work you are invited to read some press articles based upon my work.