Guido de Philippis was born in 1985. He is an analyst who contributed to Calculus of Variations, PDE’s, and Geometric Measure Theory. He obtained his master’s degree from Florence University and his PhD in November 2012 from the SNS in Pise, with advisors Luigi Ambrosio and Luis Caffarelli. After Post-Docs in Bonn and Zürich, in 2015, he got a position of Chargé de Recherches at the CNRS. A position he held at the Unité de Mathématiques Pures et Appliquées (UMPA - CNRS/ENS de Lyon). In April 2016, he became Associate Professor at SISSA (Trieste).
His main contributions are on regularity of Optimal Transport and solutions of Monge-Ampère equation, regularity issues in Geometric Measure Theory and PDE’s, quantitative stability and properties of minimizers of geometric variational problems, as well as Conservation Laws with discontinuous flux.
In particular, with A. Figalli, he showed that, in general, optimal transport maps are smooth outside a closed subset of measure zero; they also obtained an integrability property for Monge-Ampère which was open for several years; finally, they proved a conjecture of de Giorgio on the minimizers of the Mumford-Shah energy.
With L. Brasco, and B. Velichkov, Guido also established a sharper version of the Faber-Krahn inequality, which was conjectured by N. Nadirashvili. With F. Cagnetti, M. Colombo, and F. Maggi, he obtained a substantial contribution to the equality case for the Steiner symmetrization.