Professor Alessio Figalli specializes in the wide-ranging fields of Calculus of Variations and Partial Differential Equations, focusing especially on optimal transport, functional and geometric inequalities, elliptic partial differential equations, and free boundary problems. His work also extends into other areas within both pure and applied mathematics. 

Professor Alessio Figalli, born in Rome in 1984, is an Italian mathematician. After completing his Bachelor’s and Master’s degrees in mathematics at the University of Pisa, he obtained a joint PhD in mathematics between Pisa and Lyon. He held faculty positions in France and the United States before joining ETH Zürich in 2016 as a chaired professor. Since 2019, Professor Figalli has served as the director of the Institute for Mathematical Research at ETH Zürich.

Professor Figalli has received numerous prestigious awards, most notably the Fields Medal (often regarded as the Nobel Prize in mathematics) in 2018 “for contributions to the theory of optimal transport and its applications in partial differential equations, metric geometry and probability.”

He has authored over 150 international publications and serves as a scientific advisor and board member for several research institutes. He is actively involved in teaching and mentoring, and he often engages in public talks and academic conferences.

Among his other honors, Professor Figalli has been named a Knight of the Order of Merit of the Italian Republic, received several honorary doctorates, and even had asteroid 438523 named after him.

Education

•    PhD in Mathematics, Scuola Normale Superiore of Pisa, Italy and École Normale Supérieure of Lyon, France (2007)
•    Master degree in Mathematics, Scuola Normale Superiore of Pisa, Italy (2006)
•    Bachelor degree in Mathematics, Scuola Normale Superiore of Pisa, Italy (2004)

Experience

•    Director of the Institute of Mathematical Research, ETH Zürich, 2019–present.
•    Full Professor, ETH Zurich, 2016-present.
•    Full Professor and R. L. Moore Chair, The University of Texas at Austin, 2013–2016.
•    Full Professor, The University of Texas at Austin, 2011–2013.
•    Associate Professor, The University of Texas at Austin, 2010–2011.
•    Associate Professor and Harrington Faculty Fellow, The University of Texas at Austin, 2009–2010.
•    Professor, École Polytechnique, 2008–2009.
•    Researcher (Chargé de recherche CNRS), University of Nice, 2007–2008.

Awards and Honors

•    Fields Medal, 2018.
•    UIMP Medal, 2024.
•    Frontiers of Science Awards, 2023.
•    Foreign Member of the Accademia Nazionale delle Scienze detta dei XL, 2022-present
•    Falling Walls Award in Engineering and Technology, 2020.
•    Girolamo Cardano International Prize, 2020.
•    Gili Agostinelli Prize, Accademia delle Scienze di Torino, 2019.
•    Member of Academia Europaea, 2019– present 
•    Foreign Member of the Royal Spanish Academy of Sciences, 2018–present
•    Feltrinelli Prize, Accademia Nazionale dei Lincei, 2017.
•    Fellow and Honorary Member of the European Academy of Sciences, 2017– present
•    O’Donnell Award in Science, The Academy for Medicine, Engineering, & Science of Texas, 2016.
•    Stampacchia Gold Medal, Italian Mathematical Union, 2015.
•    European Mathematical Society (EMS) Prize, 2012.
•    Peccot-Vimont Prize and Cours Peccot, Collège de France, 2011–2012.
•    Gioacchino Iapichino Prize, Accademia Nazionale dei Lincei, 2010.
•    Ande Prize, Associazione Angelo Marcello Anile and Consorzio Catania Ricerche, 2010.

Most Significant Scholarly Outputs

1.    Amass transportation approach to quantitative isoperimetric inequalities (with F. Maggi and A. Pratelli), Invent. Math. 182 (2010), no. 1, 167-211. 
2.    W2,1 regularity for solutions of the Monge-Ampère equation (with G. De Philippis), Invent. Math. 192 (2013), no. 1, 55-69. 
3.    Partial regularity for optimal transport maps (with G. De Philippis), Publ. Math. Inst. Hautes Études Sci. 121 (2015), 81-112.
4.    Universality in several-matrix models via approximate transport maps (with A. Guionnet), Acta Math. 217 (2016), no. 1, 81-176. 
5.    On the fine structure of the free boundary for the classical obstacle problem (with J. Serra), Invent. Math. 215 (2019), no. 1, 311-366. 
6.    On stable solutions for boundary reactions: a De Giorgi type result in dimension 4+1 (with J. Serra), Invent. Math. 219 (2020), no. 1, 153-177. 
7.    Stable solutions to semilinear elliptic equations are smooth up to dimension 9 (with X. Cabré, X. Ros-Oton, and J. Serra), Acta Math. 224 (2020), no. 2, 187–252. 
8.    Generic regularity of free boundaries for the obstacle problem (with X. Ros-Oton and J. Serra), Publ. Math. Inst. Hautes Études Sci. 132 (2020), 181–292. 
9.    The singular set in the Stefan problem (with X. Ros-Oton and J. Serra), J. Amer. Math. Soc. 37 (2024), no. 2, 305–389. 
10.    Complete classification of global solutions to the obstacle problem (with S. Eberle and G.S. Weiss), Ann. of Math. (2) 201 (2025), no. 1, 167-224.