Research

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.

Preprint

Stratified spaces and synthetic Ricci curvature bounds, with J. Bertrand, C. Ketterer and T. Richard, available at arXiv:1804.08870.

Publications

An Obata singular theorem for stratified spaces, Trans. Amer. Math. Soc. 370 (2018), 4147-4175, available at arXiv:1511.08093.

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.

Talks