Research

Research interests

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 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.