I’ve been awarded the Oberwolfach prize 2010 (shared with L. Székelyhidi)

I’m interested in metric geometry and metric analysis

Most important research contributions:

1. Proof of the splitting theorem for spaces with non-negative Ricci curvature in the sense of Lott-Sturm-Villani ([1]). The additional requirement that the space is `infinitesimally Hilbertian’ must be imposed in order to enforce a Riemannian-like behavior of the space. The resulting notion `CD(K,N) + infinitesimal Hilbertianity’ is stable w.r.t. measured-Gromov-Hausdorff convergence.

1. Construction of a differential structure over arbitrary metric measure spaces. Over spaces with Ricci curvature bounded from below, out of this structure the notions of Laplacian, Hessian, covariant/exterior differentiation and Ricci curvature all make sense and obey the same key inequalities which are true in the smooth setting (see [2], [3])

1. Study of the heat flow on metric measure spaces (see [4], [5] - with K. Kuwada and S.-I Ohta - and [6],[7] with L. Ambrosio and G. Savaré)

1. Theory and applications of gradient flows both in abstract metric spaces and in the Wasserstein space (see the monograph co-authored with L. Ambrosio and G. Savaré published by Birkhäuser)

1. Study of the Riemannian structure of the Wasserstein space (see the monograph published by Memoirs of the AMS)

Professeur

Université Pierre et Marie Curie

(Paris 6 - Jussieu)

Institut de Mathématiques de Jussieu

Equipe d'Analyse Fonctionnelle