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.

Publications and preprints

1. (with Rodnianski) Obstruction-free gluing for the Einstein equations. arXiv:2210.09663.
2. (with Aretakis and Rodnianski) Characteristic gluing to the Kerr family and application to spacelike gluing. arXiv:2107.02456.
3. (with Aretakis and Rodnianski) The characteristic gluing problem for the Einstein vacuum equations. Linear and non-linear analysis. arXiv:2107.02449.
4. (with Aretakis and Rodnianski) The characteristic gluing problem for the Einstein equations and applications. arXiv:2107.02441.
5. (with Graf) The spacelike-characteristic Cauchy problem of general relativity in low regularity. Ann. PDE 8, 22 (2022).
6. (with Graf) The canonical foliation on null hypersurfaces in low regularity. Ann. PDE 8, 23 (2022).
7. The localised bounded $L^2$-curvature theorem. Comm. Math. Phys. 372, pages 71–90 (2019).
8. Boundary harmonic coordinates on manifolds with boundary in low regularity. Comm. Math. Phys. 371, pages 1131–1177 (2019).
9. An extension procedure for the constraint equations. Ann. PDE 4, 2 (2018).

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.

Invited talks at seminars

• 06/2023 General Relativity seminar, University of Munster
• 05/2023 Analysis seminar, ETH Zurich
• 01/2023 General Relativity seminar, University of Vienna
• 11/2022 Analysis seminar, Oxford University
• 11/2022 London PDE Seminar, Imperial College London
• 11/2022 Analysis seminar, University of Edinburgh
• 03/2022 Analysis/probability seminar, Max-Planck-Institute Leipzig
• 12/2021 Colloquium, JoMaReC
• 11/2021 Colloquium, Black Hole Initiative, Harvard University
• 11/2021 Colloquium, Gravity Initiative, Princeton University
• 10/2021 PDE and Differential Geometry seminar, UConn
• 10/2021 GR and Geometric Analysis seminar, Columbia University
• 10/2021 ICERM seminar, Brown University
• 08/2021 Relativity Seminar, University of Vienna
• 06/2021 Analysis Seminar, Caltech
• 06/2021 Summer Meeting, Canadian Mathematical Society
• 03/2021 Colloquium, University of Leipzig
• 03/2021 Research Symposium, UC Irvine
• 03/2021 AMS Eastern Sectional Meeting
• 03/2021 PDE seminar, Vanderbilt University
• 11/2020 General Relativity Webinar, Princeton University
• 10/2020 Colloquium, University Freiburg im Breisgau
• 06/2020 Canadian Mathematical Society, online (cancelled)
• 02/2020 Colloquium, University Konstanz
• 02/2019 Geometric analysis seminar, Fields Institute
• 11/2017 Analysis and Applied Math seminar, University of Toronto
• 02/2017 Pure Analysis and PDE seminar, Imperial College
• 02/2017 Geometry seminar, LMPT, Tours
• 12/2016 Mathematical Physics seminar, Institut Fourier, Grenoble
• 10/2016 General relativity seminar, Paris 6

Invited talks at workshops, conferences, and schools

• 07/2023 5h mini-course On null gluing, Domoschool 2023, Domodossola, Italy
• 07/2023 Main conference of Thematic Programme Spectral Theory and Mathematical Relativity, ESI Vienna
• 03/2023 8h mini-course On characteristic gluing, International junior scientist workshop: Mathematical GR, Tubingen
• 02/2023 3h Ringvorlesung General Relativity, MPI MIS Leipzig
• 03/2022 6h mini-course On characteristic gluing, Harvard University
• 08/2021 Mathematical Aspects of GR, MFO, Oberwolfach
• 05/2018 Initial data in general relativity, Fairbanks, Alaska