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Durham University

Department of Mathematical Sciences


The Fields Medal 2018 awarded to Alessio Figalli, Visiting Professor in the Department of Mathematical Sciences at Durham

(1 August 2018)

Alessio Figalli, Fields Medal 2018

Fields Medal 2018 (© ETH Zürich - Gian Marco Castelberg)

The Fields Medal is the world's most prestigious prize for mathematicians. It is awarded by the International Mathematical Union (IMU) once every four years, to up to four recipients under the age of 40. The selection is based both on major early-career contributions and on the promise of future achievements. Mathematicians usually receive this award for solving an outstanding open problem or for developing powerful new methods for gaining novel insights into existing areas of mathematical research. The Fields Medal is often said to be the equivalent of the Nobel Prize for Mathematicians (although there is no age limit for receiving the Nobel Prize).

There are five Fields medallists currently residing in the UK (out of 46 alive worldwide): Sir Michael Atiyah (retired Oxford/Cambridge/Edinburgh, Geometry - PhD 1955), Sir Simon Donaldson (Imperial College, Topology - PhD 1983), Sir Timothy Gowers (Cambridge, Functional Analysis - PhD 1990), Martin Hairer KBE (Imperial College, Stochastic Analysis - PhD 2001) and Caucher Birkar (Cambridge, Algebraic Geometry - PhD 2004).

 On 1st August 2018, Professor Alessio Figalli was awarded the Fields Medal at a ceremony in Rio de Janeiro at the International Congress of Mathematicians, "for his contributions to the theory of optimal transport and its applications to Partial Differential Equations, Metric Geometry and Probability".

Professor Alessio Figalli (presently ETH Zurich - PhD 2007) has made numerous seminal contributions to the broad area of Calculus of Variations and Partial Differential Equations. An important focus of his research has been the optimal transport problem: finding the best way of transporting resources from one place to another. Optimal transport, besides being an important challenging problem by itself, turns out to have also striking applications to other areas of mathematics.

Figalli has been able to use optimal transport techniques to understand how the shape of soap bubbles and crystals change under the influence of external forces. Also, by exploiting the principle that many physical phenomena evolve in time trying to minimize the total kinetic energy, he has obtained new results on the Monge-Ampère equation that have allowed him to prove global existence of solutions to the semi-geostrophic equations, a model used in meteorology to study large scale atmospheric flows.

More recently, Figalli has both introduced and developed new transportation techniques to prove universality results in certain random matrix models.

Furthermore, in a completely different direction, he has recently developed a new approach to study the structure of interfaces in phase transitions, for instance ice melting to water.


Alessio Figalli was born in Rome (Italy) in 1984. He received his master's degree in mathematics from the Scuola Normale Superiore di Pisa in 2006 and earned a joint doctorate in 2007 from the Scuola Normale Superiore di Pisa and the Ecole Normale Supérieure de Lyon, under the joint supervision of Professor Luigi Ambrosio and Professor Cedric Villani, himself a Fields medallist since 2010. In 2007 he was appointed Chargé de Recherche at the Centre National de la Recherche Scientifique (CNRS), and in 2008 he went to the Ecole Polytechnique in Paris as Professeur Hadamard. In 2009 he moved to the University of Texas at Austin as Associate Professor, becoming Full Professor in 2011, and R. L. Moore Chair holder in 2013. In 2016, he joined the mathematics department of the ETH Zurich.


Alessio has been a Visiting Professor in the Department of Mathematical Sciences at Durham since October 2017, and we enjoy his presence and scientific conversations during his frequent visits. We wish to add our heartfelt congratulations to Alessio for his remarkable and well-deserved achievement.

See an interview Alessio gave to Quanta Magazine recently.