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Doctor Honoris Causa Courtesy of ETH, Zürich of the Universitat Politècnica De Catalunya 22Nd November 2019 Alessio Figalli 1 Main Collaborators

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Doctor Honoris Causa Courtesy of ETH, Zürich of the Universitat Politècnica De Catalunya 22Nd November 2019 Alessio Figalli 1 Main Collaborators Alessio Figalli Fields Medal 2018 Courtesy of ETH, Zürich Doctor Honoris Causa of the Universitat Politècnica de Catalunya 22nd November 2019 Alessio Figalli 1 Main collaborators Ludovic Rifford, Université Nice Sophia Antipolis. Director of the Centre Guido de Philippis, Courant Institute, New York University. EMS Prize Luigi Ambrosio, Scuola Normale Superiore di Pisa. Fermat Prize 2003. Bal- International de Mathématiques Pures et Appliquées. Eisenbud Professor 2016. Stampacchia Medal 2018. Maria Colombo, EPFL Lausanne. Iapichi- zan Prize 2019. Cédric Villani, Institut Henri Poincaré, Sorbone University, at MSRI 2013 (fall). Enrico Valdinoci, University of Western Australia. no Prize 2016. Miranda Prize 2018. Begoña Barrios, Universidad de La La- University of Lyon, Institut Camille-Jordan. EMS Prize 2008. Fermat Prize Most cited mathematician according to his graduation year (in all sub- guna, Tenerife, Spain. Xavier Ros-Oton, Universität Zürich. RSME Rubio 2009. Fields Medal 2010. Doob Prize 2014. Luis A. Caffarelli, University of jects and in Analysis). ERC Starting Grant 2011-2016. Aldo Pratelli, Univer- de Francia Prize 2016. SeMA Antonio Valle Prize 2017. ERC Starting Grant Texas at Austin. Steele Prize 2009. Wolf Prize 2012. Shaw Prize 2018. Jean 2018. Fundación Princesa de Girona Prize 2019. Joaquim Serra, ETH Zü- sità di Pisa. Medal of the President of Italian Republic for young research- Bourgain (1954-2018). Fields Medal 1994. Shaw Prize 2010. Crafoord Prize rich. SCM Évariste Galois Prize 2011. SCM Josep Teixidó Prize 2016. SeMA ers 2004. Iapichino Prize 2005. ERC Starting Grant 2010-2015. Miranda 2012. Steele Prize 2018. Antonio Valle Prize 2019. RSME Rubio de Francia Prize 2019. Prize 2011. De Giorgi’s Prize 2015. Matteo Bonforte, Universidad Autóno- ma de Madrid. Álvaro Pelayo, University of California at San Diego. RSME Rubio de Francia Prize 2009. NSF Faculty CAREER Award 2016. David Jerison, Massachusetts Institute of Technology. Bergman Prize 2012. Moon-Jin Kang, Sookmyung Women's University, Seoul, South Korea. Juan L. Vázquez, Universidad Autónoma de Madrid. Premio Nacional de In- Emanuel Indrei, Department of Mathematics, Purdue University. Connor vestigación Julio Rey Pastor 2003. Plenary speaker at ICM-2006. Medalla Mooney, University of California at Irvine. Firestone Medal for Excel- Marco Di Francesco, Dipartimento di Ingegneria e Scienze dell’Informa- de la RSME 2018. Albert Fathi, Georgia Institute of Technology. Sophie Ger- lence in Undergraduate Research, Stanford University, 2011. Yash Jha- zione e Matematica, Università degli Studi dell’Aquila. Dejan Slepčev, De- veri, Princeton Institute for Advanced Study. Robin Neumayer, North- main Prize 2013. Professeur émérite à l’ENS de Lyon. Paul Thierry, Di- partment of Mathematical Sciences, Carnegie Mellon University. Giulio western University. Xavier Fernández-Real, PhD student, ETH Zürich. recteur de Recherche, Centre de Mathématiques Laurent Schwartz, École Ciraolo, Department of Mathematics Federigo Enriques, Università de- Whelan Prize in Mathematics from Christ's College, University of Cam- Polytechnique, Paris, France. Henrik Shahgholian, Royal Institute of Tech- gli Studi di Milano. Nicola Gigli, Scuola Internazionale Superiore di Studi bridge, 2015. SCM Évariste Galois Prize 2016. National Award for Excel- nology (KTH), Stockholm, Sweden. Avanzati. De Giorgi’s Prize 2019. Laura Valentina Spinolo, IMATI-CNR, Pa- lence in Academic Performance 2013-14, First Prize, 2018. via, Italy. Xavier Cabré, ICREA Research Professor, Department of Mathematics, Universitat Politècnica de Catalunya. Kurt Friedrichs Prize, New York University, 1995. Har- rington Faculty Fellow, The University of Texas at Aus- tin, 2001-02. Fellow of the American Mathematical Society, inaugural class, 2012. Francesco Maggi, University of Texas at Austin. Miranda Prize 2008. José A. Carrillo de la Plata, Imperial College London. Von Mises Prize 2006. Wolfson Prize 2012. Robert J. McCann, University of Toronto. Coxeter- James Prize 2005. Jeffery-Williams Prize 2017. Alice Guionnet, École Nor- male Supérieure de Lyon. Loève Prize 2009. Pascal Medal 2018. Kim Young -Heon, University of British Columbia. Alessio Figalli 2 Work 1/3 La physique mathématique et l’analyse pure ne sont pas seulement des (Grundlehren der Mathematischen Wissenschaften 338. Springer-Verlag, 2015 AF, Gonzalo Contreras and Ludovic Rifford. “Generic hyperbolicity puissances limitrophes, entretenant des rapports de bon voisinage : elles 2009. xxii+973 pp)”. Bulletin of the AMS (N.S.) 47.4, 723-727. of Aubry sets on surfaces”. Inventiones Mathematicae 200.1, 201-261. se pénètrent mutuellement et leur esprit est le même. 2010 AF and Albert Fathi. “Optimal transportation on non-compact man- Henri Poincaré, La Valeur de la Science. 2016 AF and Alice Guionnet. “Universality in several-matrix models via ifolds”. Israel Journal of Mathematics 175.1, 1-59. approximate transport maps”. Acta Mathematica. 217.1, 81-176. 2010 AF. "The optimal partial transport problem." Archive for rational Large random matrices arise as a natural model in diverse fields such as Sources mechanics and analysis 195.2: 533-560. quantum mechanics, quantum chaos, telecommunications, finance, and 2010 AF, and Ludovic Rifford. “Mass transportation on sub-Riemannian statistics. The central mathematical question in this area is how much their ▪ Alessio Figalli (AF) Web page (WP), particularly his CV (22.10.2019). Manifolds”. Geometric and Functional Analysis 20.1, 124-159. asymptotic properties depend on the fine details of the model. […] About ▪ Luis Caffarelli (LC). “Alessio Figalli: His Contributions to Geometry and the universality of the fluctuations of the eigenvalues in several-matrix 2010 AF and Kim Young-Heon. “Partial regularity of Brenier solutions of Analysis”. Proceedings of the International Congress of Mathematicians. models, little was known except in very particular situations. […] developed the Monge-Ampère equation”. Discrete and Continuous Dynamical Sys- World Scientific, 2019. Volume 1, 43-46. a new approach to these questions by introducing particular approximate tems 28.2: 559-565. transport maps. […] This is a real breakthrough, which in addition, gives a A recurring theme in Figalli's research is the interaction between the theo- firm mathematical grounding to the widely held belief coming from physics ry of optimal transport and other areas of mathematics. Optimal transport 2010 AF, Francesco Maggi and Aldo Pratelli: “A mass transportation ap- proach to quantitative isoperimetric inequalities”. Inventiones Mathe- that a universality of local fluctuations holds, at least until some phase theory, although pioneered by G. Monge back in 1781, has emerged to transition occurs. (LC, p.2-3 (44-45). paramount importance in many areas of mathematics only in the last two maticae 182.1, 167-211. 2016 AF, Diogo Gomes and Diego Marcon. “Weak KAM theory for a decades. One of the most valuable features of this theory is its unifying … a sharp quantitative stability theorem for the Wulff inequality […] a most power, in the sense that key ideas and constructions in optimal transport important mathematical result in our understanding of surface tension weakly coupled system of Hamilton–Jacobi equations”. Calculus of Varia- have turned out to be useful in the most unexpected contexts. Figalli is driven phase transitions, as it relates the microscopic structure of a given tions and Partial Differential Equations 55.4: 55-79. currently one of the most authoritative experts in optimal transport and its surface tension energy density to the macroscopic shape of the liquid/ many applications. (LC, p. 1 (43)) crystal observed at equilibrium. […] its sharp stability version allows one 2017 AF and David Jerison. “Quantitative stability for the Brunn– ▪ Xavier Ros-Oton and Joaquim Serra. Private communications. to describe in quantitative terms every low energy state. This is a result of Minkowski inequality”. Advances in Mathematics 314: 1-47. clear physical importance, whose proof required several original and inno- ▪ MathSciNet. […] succeeded in the quite challenging task of combining tools from addi- vative mathematical ideas. (LC, p. 1-2 (4344)) tive combinatorics, affine geometry, harmonic analysis and optimal ▪ FME. Documentation on theDHC nomination of AF. transport to obtain the first quantitative stability result for the BM inequali- 2011* AF, William Bench, Carlo De Franchis, Laurent Deproit, Sébastien ty in arbitrary dimension and on generic sets. […] quite impressive, both for Gilles, Byunghyun Oh, Adrien Tenne, Kevin Webster. Autour des inégali- the technical complexity, the wealth of original ideas involved, and the Topics tés isopérimétriques. Éditions de l’École Polytechnique, Palaiseau. 124 p. mathematical beauty of the question under consideration (LC, p. 2 (44)). 2011 AF and Francesco Maggi. “On the shape of liquid drops and crystals 2017 AF, Brian Krummel and Xavier Ros-Oton. “On the regularity of the While the broad research area of AF is Partial Differential Equations in the small mass regime”. Archive for Rational Mechanics and Analysis free boundary in the p-Laplacian obstacle problem”. Journal of Differen- and Calculus of Variations, he has landmark contributions in a large 201.1, 143-207. tial Equations 263.3: 1931-1945. number of topics, like Regularity of solutions to elliptic PDE's and to 2017* AF. The Monge–Ampère equation and its applications. EMS, 2017. free boundary problems; Isoperimetric and geometric
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