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.
An upper bound on the revised first Betti number and a torus stability result for RCD spaces, with A. Mondino and R. Perales, available at arXiv:2104.06208.
Limits of manifolds with a Kato bound on the Ricci curvature, with G. Carron and D. Tewodrose, available at arXiv:2102.05940.
Non existence of Yamabe minimizers on singular spheres, with K. Akutagawa, available at arXiv:1909.09367.
Sphere theorems for RCD and stratified spaces, with S. Honda, to appear in the Annali della Scuola Normale di Pisa, available at arXiv:1907.03482
Stratified spaces and synthetic Ricci curvature bounds, with J. Bertrand, C. Ketterer and T. Richard, to appear in the Annales de l’Institut Fourier, 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.