Alessio Figalli (; born 2 April 1984) is an Italian

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

working primarily on the

calculus of variations The calculus of variations (or variational calculus) is a field of mathematical analysis that uses variations, which are small changes in Function (mathematics), functions and functional (mathematics), functionals, to find maxima and minima of f ...

and

partial differential equation In mathematics, a partial differential equation (PDE) is an equation which involves a multivariable function and one or more of its partial derivatives. The function is often thought of as an "unknown" that solves the equation, similar to ho ...

s. He was awarded the Peccot-Vimont Prize and the Peccot Lectures in 2012, the EMS Prize in 2012, the Stampacchia Medal in 2015, the

Feltrinelli Prize The Feltrinelli Prize (from the Italian "Premio Feltrinelli", also known as "International Feltrinelli Prize" or "Antonio Feltrinelli Prize") is an award for achievement in the arts, music, literature, history, philosophy, medicine, and physical a ...

in 2017, and the

Fields Medal The Fields Medal is a prize awarded to two, three, or four mathematicians under 40 years of age at the International Congress of Mathematicians, International Congress of the International Mathematical Union (IMU), a meeting that takes place e ...

in 2018. He was an

invited speaker at the International Congress of Mathematicians An invitation system is a method of encouraging people to join an organization, such as a Club (organization), club or a website. In regular society, it refers to any system whereby new members are chosen; they cannot simply apply. In relation to w ...

2014. In 2016 he was awarded a

European Research Council The European Research Council (ERC) is a public body for funding of scientific and technological research conducted within the European Union (EU). Established by the European Commission in 2007, the ERC is composed of an independent Scientific ...

(ERC) grant, and in 2018 he received the Doctorate ''Honoris Causa'' from the Université Côte d'Azur. In 2019, he received the Doctorate ''Honoris Causa'' from the Polytechnic University of Catalonia.

Biography

Figalli received his master's degree from the

University of Pisa The University of Pisa (, UniPi) is a public university, public research university in Pisa, Italy. Founded in 1343, it is one of the oldest universities in Europe. Together with Scuola Normale Superiore di Pisa and Sant'Anna School of Advanced S ...

in 2006 (as a student of the

Scuola Normale Superiore di Pisa The Scuola Normale Superiore (commonly known in Italy as "la Normale") is a public university in Pisa and Florence, Tuscany, Italy, currently attended by about 600 undergraduate and postgraduate (PhD) students. Together with the University of Pi ...

), and earned his doctorate in 2007 under the supervision of

Luigi Ambrosio Luigi Ambrosio (born 27 January 1963) is a professor at Scuola Normale Superiore in Pisa, Italy. His main fields of research are the calculus of variations and geometric measure theory. Biography Ambrosio entered the Scuola Normale Superiore d ...

at the

and

Cédric Villani Cédric Patrice Thierry Villani (; born 5 October 1973) is a French politician and mathematician working primarily on partial differential equations, Riemannian geometry and mathematical physics. He was awarded the Fields Medal in 2010, and he ...

at the École Normale Supérieure de Lyon. In 2007, he was appointed Chargé de recherche at the

French National Centre for Scientific Research The French National Centre for Scientific Research (, , CNRS) is the French state research organisation and is the largest fundamental science agency in Europe. In 2016, it employed 31,637 staff, including 11,137 tenured researchers, 13,415 engi ...

, and in 2008 he went to the

École polytechnique (, ; also known as Polytechnique or l'X ) is a ''grande école'' located in Palaiseau, France. It specializes in science and engineering and is a founding member of the Polytechnic Institute of Paris. The school was founded in 1794 by mat ...

as Professeur Hadamard. In 2009, he moved to the

University of Texas at Austin The University of Texas at Austin (UT Austin, UT, or Texas) is a public university, public research university in Austin, Texas, United States. Founded in 1883, it is the flagship institution of the University of Texas System. With 53,082 stud ...

as an associate professor. He became full professor in 2011, and R. L. Moore Chair holder in 2013. Since 2016, he is a chaired professor at

ETH Zürich ETH Zurich (; ) is a public university in Zurich, Switzerland. Founded in 1854 with the stated mission to educate engineers and scientists, the university focuses primarily on science, technology, engineering, and mathematics. ETH Zurich ra ...

. Amongst his several recognitions, Figalli has won an EMS Prize in 2012, he has been awarded the Peccot-Vimont Prize 2011 and Cours Peccot 2012 of the

Collège de France The (), formerly known as the or as the ''Collège impérial'' founded in 1530 by François I, is a higher education and research establishment () in France. It is located in Paris near La Sorbonne. The has been considered to be France's most ...

and has been appointed Nachdiplom Lecturer in 2014 at

. He has won the 2015 edition of the Stampacchia Medal, and the 2017 edition of the

for mathematics. In 2018, he won the

"for his contributions to the theory of optimal transport, and its application to partial differential equations, metric geometry, and probability".

Work

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 equation In mathematics, a (real) Monge–Ampère equation is a nonlinear second-order partial differential equation of special kind. A second-order equation for the unknown function ''u'' of two variables ''x'',''y'' is of Monge–Ampère type if it is l ...

s. 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 and a partial regularity result for Monge–Ampère type equations, both proved together with Guido de Philippis. He used optimal transport techniques to get improved versions of the anisotropic

isoperimetric inequality In mathematics, the isoperimetric inequality is a geometric inequality involving the square of the circumference of a closed curve in the plane and the area of a plane region it encloses, as well as its various generalizations. '' Isoperimetric'' ...

, 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 anisotropic

. Then, in a joint work with Eric Carlen, he addressed the stability analysis of some Gagliardo–Nirenberg and logarithmic Hardy–Littlewood–Sobolev inequalities to obtain a quantitative rate of convergence for the critical mass Keller–Segel equation. He also worked on

Hamilton–Jacobi equation In physics, the Hamilton–Jacobi equation, named after William Rowan Hamilton and Carl Gustav Jacob Jacobi, is an alternative formulation of classical mechanics, equivalent to other formulations such as Newton's laws of motion, Lagrangian mecha ...

s and their connections to weak Kolmogorov–Arnold–Moser theory. In a paper with Gonzalo Contreras and Ludovic Rifford, he proved generic hyperbolicity of Aubry sets on compact surfaces. In addition, he has given several contributions to the Di Perna–Lions' theory, applying it both to the understanding of semiclassical limits of the

Schrödinger equation The Schrödinger equation is a partial differential equation that governs the wave function of a non-relativistic quantum-mechanical system. Its discovery was a significant landmark in the development of quantum mechanics. It is named after E ...

with very rough potentials, and to study the Lagrangian structure of weak solutions to the Vlasov–Poisson equation. More recently, in collaboration with Alice Guionnet, he introduced and developed new transportation techniques in the topic of

random matrices In probability theory and mathematical physics, a random matrix is a matrix-valued random variable—that is, a matrix in which some or all of its entries are sampled randomly from a probability distribution. Random matrix theory (RMT) is the ...

to prove universality results in several-matrix models. Also, together with Joaquim Serra, he proved the De Giorgi's conjecture for boundary reaction terms in dimension lower than five, and he improved the classical results by

Luis Caffarelli Luis Ángel Caffarelli (; born December 8, 1948) is an Argentine-American mathematician. He studies partial differential equations and their applications. Caffarelli is a professor of mathematics at the University of Texas at Austin, and the win ...

on the structure of singular points in the obstacle problem.

Books

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References

External links

Prof. Dr. Alessio Figalli, Website at ETH Zurich
{{DEFAULTSORT:Figalli, Alessio 1984 births Fields Medalists Living people 21st-century Italian mathematicians Italian mathematical analysts Academic staff of ETH Zurich Variational analysts European Research Council grantees Scientists from Rome University of Pisa alumni Scuola Normale Superiore di Pisa alumni École Normale Supérieure alumni University of Texas at Austin faculty