Research:
Einstein's general theory of relativity provides a natural arena for fundamental problems in differential geometry and PDE analysis. I am interested in the initial value problem of the Einstein equations, stability of black hole spacetimes and quasi-local mass in general relativity.
In particular, as it turned out, I invested several years of my career in studying the black hole stability problem with axial symmetry. Together with Vincent Moncrief, I developed a Hamiltonian approach to study this problem. The main difficulty is that in axial symmetry, the Weyl-Papapetrou (WP) gauge gives powerful the wave map structure but also causes serious regularity issues for the Cauchy problem.
Please read the expository article `Energy extraction or lack thereof' (open access) for more details about my work in this direction.
Furthermore, I work on the cosmic censorship conjectures, especially for the Einstein equations with U(1) symmetry, which is a direction I have been pursuing since my PhD.
I took a break from research in the time period 2022-2025.
Employment History:
September 2024 - present, Visiting Assistant Professor, College of the Holy Cross
August 2021 - May 2024, Visiting Assistant Professor, Clark University
August 2018 - June 2020 (on leave Fall 2019), Postdoctoral Fellow, Center for Mathematical Sciences and Applications, Harvard University
July 2015 - July 2018, Postdoctoral Fellow and Associate, Department of Mathematics, Yale University
July 2014 - June 2015, Postdoctoral Lecturer, Department of Mathematics, Johns Hopkins University
January 2014 - June 2014, Junior Scientist, Albert Einstein Institute (Golm)
January 2014, Dr. rer. nat. (equivalent to a PhD), Freie Universitaet Berlin; also affiliated with the Albert Einstein Institute (Golm) and the Berlin Mathematical School
August 2009, M.Sc., Department of Mathematics, Universitaet Karlsruhe (currently Karlsruhe Institute of Technology)
Recent Academic Honors:
Provost's Supplementary Research Award (2025), College of the Holy Cross
Shanahan Award of Scholarship (2025), Department of Mathematics, College of the Holy Cross
J.D. Power Center Research Associates Grant (Fall 2025)
Get in touch at [nlastname@holycross.edu]