From September 2015 to January 2018 I was a post-doc in the Geometry group of the Université Libre de Bruxelles, under the supervision of Joel Fine.
From September 2011 to August 2015 I prepared my Ph.D at the University of Cergy-Pontoise under the supervision of O. Druet et E. Hebey.
Nonlinear Analysis -- Riemannian Einstein metrics -- Constraint equations in General Relativity
In English, with a list of the talks I have given and a teaching record. Link.
Publications in peer-reviewed journals
(With J. Vétois) Compactness of sign-changing solutions to scalar curvature-type equations with bounded negative part, 36 pages, 2018. Accepted for publication in the Journal of Differential Equations. File.
(With J. Fine) Examples of compact Einstein four-manifolds with negative curvature, 57 Page, 2018. Accepted for publication in the Journal of the American Mathematical Society. arXiv:1802.00608.
(With P.D. Thizy) Bubbling above the threshold of the scalar curvature in dimensions four and five, 41 pages, 2017. Accepted for publication in Calculus of Variations and Partial Differential Equations. hal-01805092
A pointwise finite-dimensional reduction method for Einstein-Lichnerowicz-type systems: the six-dimensional case, Nonlinear Analysis 172 (2018), pp. 200–215. File
A pointwise finite-dimensional reduction method for a fully coupled system of Einstein-Lichnerowicz type, Communications in Contemporary Mathematics 20 (2018), no. 6, 1750076, 72 pp. arXiv:1605.05468.
(With J. Wei) Non-compactness and infinite number of conformal initial data sets in high dimensions, Journal of Functional Analysis 270 (2016), no.2, 718-747. arXiv:1505.02806
Stability and instability of the n-dimensional Einstein-Lichnerowicz constraints system, International Mathematics Research Notices, Vol. 2016 no.8, 1951-2025. arXiv:1502.04233
(With O. Druet) Stability of the Einstein-Lichnerowicz constraint system, Matematische Annalen 362 (2015), no.3, 839-886. arXiv:1312.6574
Effective multiplicity for the Einstein-calar field Lichnerowicz equation, Calculus of Variations and Partial Differential Equations 53 (2015) no.1, 29-64. arXiv:1307.2416
The Einstein-scalar field constraint system in the positive case, Communications in Mathematical Physics 326 (2014), no. 2, 543-557. arXiv:1301.5792
A pointwise finite-dimensional reduction method for Einstein-Lichnerowciz type systems. Proceedings of the BruTo PDE's Conference (Torino, 2-5 May 2016). To appear in the Rendiconti del Seminario Matematico - Università e Politecnico di Torino.