Research

In my research I use tools from analysis, PDE theory and differential geometry to study fundamental problems of general relativity.
More specifically, I have been working on the following topics:

• Construction and analysis of spacelike initial data for the Einstein equations.
• Control of solutions to the null structure equations, with sharp estimates in low-regularity geometric function spaces.
• Solving the Einstein equations in low-regularity (continuation results, blow-up criteria).
• Gluing problems for characteristic and spacelike initial data.

Research group

There are opportunities to join my research group by writing a Bachelor's and Master's thesis, or come in as Ph.D. student or post-doc. For the latter two, the International Max Planck Research School (IMPRS) can be found here.

Publications and preprints

1. (with Rodnianski) Obstruction-free gluing for the Einstein equations. arXiv:2210.09663, 81 pages.
2. (with Aretakis and Rodnianski) Characteristic gluing to the Kerr family and application to spacelike gluing. arXiv:2107.02456, 88 pages.
3. (with Aretakis and Rodnianski) The characteristic gluing problem for the Einstein vacuum equations. Linear and non-linear analysis. arXiv:2107.02449, 102 pages.
4. (with Aretakis and Rodnianski) The characteristic gluing problem for the Einstein equations and applications. arXiv:2107.02441, 31 pages.
5. (with O. Graf) The spacelike-characteristic Cauchy problem of general relativity in low regularity. arXiv:1909.07355, 91 pages; accepted in Ann. PDE.
6. (with O. Graf) The canonical foliation on null hypersurfaces in low regularity. arXiv:1909.07345, 69 pages; accepted in Ann. PDE.
7. The localised bounded $L^2$-curvature theorem. Comm. Math. Phys. (2019), 20 pages.
8. Boundary harmonic coordinates on manifolds with boundary in low regularity. Comm. Math. Phys. (2019), 47 pages.
9. An extension procedure for the constraint equations. Ann. PDE (2018), 4:2, 122 pages.

Theses

• The Cauchy problem in general relativity, Ph.D. thesis, UPMC (Paris 6), 2017, 259 pages.
• On the static metric extension problem (here), Master’s thesis at ETH Zurich, 2014, 21 pages.

Selected conferences and seminars

• American Mathematical Society
• Black Hole Initiative @ Harvard University
• Brown University
• Caltech
• Canadian Mathematical Society
• Columbia University
• Fairbanks, Alaska
• Fields Institute
• Freiburg University
• Gravity Initiative @ Princeton University
• Imperial College London (2 hours)
• Institut Fourier @ Grenoble
• Laboratoire de Mathématiques et Physique Théorique @ Tours
• Leipzig University
• MFO, Oberwolfach
• Oxford University
• Paris 6 (Université Pierre-et-Marie-Curie)
• UC Irvine
• UConn
• University of Edinburgh
• University of Konstanz
• University of Miami
• University of Toronto
• University of Vienna
• Vanderbilt University