I am a Postdoc in mathematics, working with Andras Vasy.
My personal webpage including teaching information: http://web.stanford.edu/~oliverlp/.
Doctor of Philosophy, University of Potsdam (2018)
Master of Science, Royal Institute of Technology (2014)
Bachelor of Science, Royal Institute of Technology (2014)
Andras Vasy, Postdoctoral Faculty Sponsor
Current Research and Scholarly Interests
My research is in Geometric Analysis, with emphasis on the following two topics:
1. Wave equations near horizons in general relativity. This amounts to a study of singular and degenerate hyperbolic PDEs on Lorentzian spacetimes. There are natural geometric applications related to the strong cosmic censorship in cosmology and the black hole uniqueness conjecture.
2. Ricci flow on non-compact manifolds. Together with Klaus Kröncke in Hamburg, we work on stability questions for Ricci flow on manifolds with a prescribed asymptotic structure at infinity. This requires a good understanding of parabolic equations on non-compact manifolds.
Preprints and publications:
- Long-time estimates for heat flows on ALE manifolds Preprint: arXiv 2006.06662. 2020
- Wave equations with initial data on compact Cauchy horizons Analysis and PDE. To appear. 2020
- Mean Curvature Flow in Asymptotically Flat Product Spacetimes The Journal of Geometric Analysis. To appear. 2020
- Extension of Killing vector fields beyond compact Cauchy horizons Preprint: arXiv 1903.09135. 2019
- On the Cauchy problem for the linearised Einstein equation Ann. Henri Poincaré 20 (2019), no.12 2019
- Symmetries of vacuum spacetimes with compact Cauchy horizons of constant non-zero surface gravity Preprint: arXiv 1809.02580. 2018
- The mode solution of the wave equation in Kasner spacetimes and redshift Math. Phys. Anal. Geom. 19 (2016), no. 4. 2016