2 April 1984 |
|Institutions||University of Texas, Austin|
|Alma mater||Scuola Normale Superiore di Pisa
École normale supérieure de Lyon
|Doctoral advisor||Luigi Ambrosio
|Doctoral students||Eric Baer, Emanuel Indrei|
|Notable awards||EMS Prize (2012)|
Figalli received his master degree in mathematics from the Scuola Normale Superiore di Pisa in 2006, and earned his doctorate in 2007 under the supervision of Luigi Ambrosio at the Scuola Normale Superiore di Pisa and Cédric Villani at the École Normale Supérieure de Lyon. In 2007 he was appointed Chargé de recherche at the French National Centre for Scientific Research, in 2008 he went to the École polytechnique as Professeur Hadamard. He has been a professor at University of Texas at Austin since 2009. Starting from 2013 he holds the R. L. Moore Chair.
Figalli has worked in the theory of optimal transport, with particular emphasis on the regularity theory of optimal transport maps and its connections to Monge–Ampère equations. Amongst the results he obtained in this direction, there stands out an important higher integrability property of the second derivatives of solutions to the Monge–Ampère equation, that he proved together with Guido De Philippis. He used optimal transport techniques to obtain improved versions of the anisotropic isoperimetric inequality, and obtained several other important result on the stability of functional and geometric inequalities. In particular, together with Francesco Maggi and Aldo Pratelli, he proved a sharp quantitative version of the anisotropic isoperimetric inequality. He also worked on Hamilton–Jacobi equations and their connections to weak KAM theory.
- "6th European Congress of Mathematics". European mathematical Society. Retrieved 13 March 2013.
- "W 2,1 regularity for solutions of the Monge–Ampère equation". Inventiones Mathematicae. Retrieved 13 June 2013.
- "A mass transportation approach to quantitative isoperimetric inequalities". Inventiones Mathematicae. Retrieved 13 June 2013.