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.