I am interested in geometric analysis, in conformal geometry, in the Yamabe problem, and in the study of singular spaces through tools of Riemannian geometry.
During my Ph.D. I studied a conformal invariant, the local Yamabe constant, which plays an important role in the solution of the Yamabe problem on metric spaces, and in particular on stratified spaces. This lead me to extend to stratified spaces some classical results of Riemannian geometry, such as the Lichnerowicz theorem for the first non-zero eigenvalue of the Laplacian and Myer’s diameter theorem.
During my Master thesis, I worked on the Schrödinger equation with fractional Laplacian and on its discretization.
Kato meets Bakry-Émery, with G. Carron et D. Tewodrose, available at arXiv:2305.07428.
Limits of manifolds with a Kato bound on the Ricci curvature. II, with G. Carron et D. Tewodrose, available at arXiv:2205.01956.
Limits of manifolds with a Kato bound on the Ricci curvature, with G. Carron and D. Tewodrose, to appear in Geometry and Topology, available at arXiv:2102.05940.
Torus stability under Kato bounds on the Ricci curvature, with G. Carron et D. Tewodrose, accepted by the Journal of the London Mathematical Society, disponible sur arXiv:2207.05419.
Non existence of Yamabe minimizers on singular spheres, with K. Akutagawa, to appear in The Journal of Geometric Analysis, available at arXiv:1909.09367.
An upper bound on the revised first Betti number and a torus stability result for RCD spaces, with A. Mondino and R. Perales, to appear in Commentarii Mathematici Helvetici, available at arXiv:2104.06208.
Stratified spaces and synthetic Ricci curvature bounds, with J. Bertrand, C. Ketterer and T. Richard, Ann. Inst. Fourier (Grenoble) 71 (2021), no. 1, 123-173, available at arXiv:1804.08870.
The Local Yamabe constant of Einstein Stratified Spaces, Annales de l’Institut Henri Poincaré Analyse Non Linéaire. 34 (2017), no.1 249-275, available at arXiv:1411.7996.
(In French) Structure des limites de variétés à courbure de Ricci minorée, d’après J. Cheeger, W. Jiang and A. Naber, d’après J. Cheeger, W. Jiang and A. Naber, Bourbaki seminar.