Alessio Figalli | |
|---|---|
.jpg) Figalli in 2019 | |
| Born | (1984-04-02)2 April 1984 (age 41) Rome, Italy |
| Alma mater | University of Pisa Scuola Normale Superiore di Pisa École normale supérieure de Lyon |
| Spouse | Mikaela Iacobelli |
| Awards | Peccot Lectures (2012) EMS Prize (2012) Stampacchia Medal (2015) Feltrinelli Prize (2017) Fields Medal (2018) |
| Scientific career | |
| Fields | Mathematics |
| Institutions | ETH Zurich University of Texas at Austin École Polytechnique University of Nice Sophia Antipolis |
| Thesis | Optimal transportation and action-minimizing measures (2007) |
| Doctoral advisor | Luigi Ambrosio Cédric Villani |
| Doctoral students | |
Alessio Figalli (Italian:[aˈlɛssjofiˈɡalli]; born 2 April 1984) is an Italianmathematician working primarily on thecalculus of variations andpartial differential equations.
He was awarded the Peccot-Vimont Prize and thePeccot Lectures in 2012, theEMS Prize in 2012,[1] theStampacchia Medal in 2015,[2] theFeltrinelli Prize in 2017, and theFields Medal in 2018. He was aninvited speaker at the International Congress of Mathematicians 2014.[3]In 2016 he was awarded aEuropean Research Council (ERC) grant, and in 2018 he received the DoctorateHonoris Causa from theUniversité Côte d'Azur. In 2019, he received the DoctorateHonoris Causa from thePolytechnic University of Catalonia.
Figalli received his master's degree from theUniversity of Pisa[4] in 2006 (as a student of theScuola Normale Superiore di Pisa), and earned his doctorate in 2007 under the supervision ofLuigi Ambrosio at theScuola Normale Superiore di Pisa andCédric Villani at theÉcole Normale Supérieure de Lyon. In 2007, he was appointed Chargé de recherche at theFrench National Centre for Scientific Research, and in 2008 he went to theÉcole polytechnique as Professeur Hadamard.[5]
In 2009, he moved to theUniversity of Texas at Austin as an associate professor. He became full professor in 2011, andR. L. Moore Chair holder in 2013. Since 2016, he is a chaired professor atETH Zürich.[5]
Amongst his several recognitions, Figalli has won anEMS Prize in 2012, he has been awarded the Peccot-Vimont Prize 2011 and Cours Peccot 2012 of theCollège de France and has been appointed Nachdiplom Lecturer in 2014 atETH Zürich.[6] He has won the 2015 edition of theStampacchia Medal, and the 2017 edition of theFeltrinelli Prize for mathematics.
In 2018, he won theFields Medal "for his contributions to the theory of optimal transport, and its application to partial differential equations, metric geometry, and probability".[7]
Figalli has worked in the theory ofoptimal transport, with particular emphasis on the regularity theory of optimal transport maps and its connections toMonge–Ampère equations. Amongst the results he obtained in this direction, there stand out an important higher integrability property of the second derivatives of solutions to the Monge–Ampère equation[8] and a partial regularity result for Monge–Ampère type equations,[9] both proved together withGuido de Philippis. He used optimal transport techniques to get improved versions of the anisotropicisoperimetric inequality, and obtained several other important results 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 anisotropicisoperimetric inequality.[10]
Then, in a joint work withEric Carlen, he addressed the stability analysis of someGagliardo–Nirenberg and logarithmicHardy–Littlewood–Sobolev inequalities to obtain a quantitative rate of convergence for the critical mass Keller–Segel equation.[11] He also worked onHamilton–Jacobi equations and their connections to weakKolmogorov–Arnold–Moser theory. In a paper with Gonzalo Contreras and Ludovic Rifford, he proved generic hyperbolicity of Aubry sets on compact surfaces.[12]
In addition, he has given several contributions to the Di Perna–Lions' theory, applying it both to the understanding ofsemiclassical limits of theSchrödinger equation with very rough potentials,[13] and to study the Lagrangian structure of weak solutions to theVlasov–Poisson equation.[14] More recently, in collaboration withAlice Guionnet, he introduced and developed new transportation techniques in the topic ofrandom matrices to prove universality results in several-matrix models.[15] Also, together with Joaquim Serra, he proved theDe Giorgi's conjecture for boundary reaction terms in dimension lower than five, and he improved the classical results byLuis Caffarelli on the structure of singular points in theobstacle problem.[16]
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