Alessio Figalli

Alessio Figalli
Figalli in 2019
Alessio Figalli
Born	2 4, 1984
Birthplace	Rome, Italy
Nationality	Italian
Occupation	Mathematician
Employer	ETH Zurich
Known for	Calculus of variations, partial differential equations, optimal transport
Education	PhD in Mathematics (2007)
Awards	Fields Medal (2018), EMS Prize (2012), Feltrinelli Prize (2017)
Website	[https://people.math.ethz.ch/~afigalli/ Official site]

Alessio Figalli (born 2 April 1984) is an Italian mathematician whose work in the calculus of variations, partial differential equations, and optimal transport has placed him among the most recognized mathematicians of his generation. Born in Rome, Figalli developed his mathematical talents through studies in Italy and France before embarking on an academic career that has taken him across Europe and the United States. He was awarded the Fields Medal in 2018 — often described as the highest honor in mathematics — for his contributions to the theory of optimal transport and its applications to problems in partial differential equations, metric geometry, and probability. His research has addressed questions ranging from the stability of crystal shapes to the mathematical behavior of clouds and weather patterns. As of 2025, Figalli holds a professorship at ETH Zurich, where he has been based since 2016.

Early Life

Alessio Figalli was born on 2 April 1984 in Rome, Italy. Growing up, Figalli did not initially envision a career in mathematics. In an interview with the European Research Council (ERC) following his Fields Medal win, Figalli recalled: "Growing up I didn't even know that mathematicians existed!" This candid reflection underscored the degree to which his path into mathematics was not a foregone conclusion but rather a discovery made through education and exposure to the discipline.

Figalli's early mathematical development took a significant turn during his formative academic years in Italy. According to a profile in Quanta Magazine, Figalli was a student who found his way to mathematics somewhat gradually, without the prodigy narrative that characterizes some Fields Medal recipients. He has spoken of how his interests sharpened as he encountered more advanced mathematical ideas, and how the Italian educational system, with its emphasis on rigorous training in analysis and geometry, helped shape his trajectory.

Figalli's early life in Rome provided him with a cultural and intellectual environment that would later complement his mathematical career. His path from a childhood in the Italian capital to the highest echelons of international mathematics reflects both the opportunities afforded by the European academic system and Figalli's own evolving commitment to mathematical research.

Education

Figalli pursued his undergraduate studies at the University of Pisa and the Scuola Normale Superiore di Pisa, two of Italy's most prestigious institutions for mathematics and the sciences. The Scuola Normale Superiore, in particular, has a long tradition of producing leading Italian mathematicians, and Figalli's time there provided a rigorous foundation in mathematical analysis.

For his doctoral studies, Figalli pursued a joint program between the Scuola Normale Superiore di Pisa and the École normale supérieure de Lyon in France. He completed his PhD in 2007 with a thesis titled Optimal transportation and action-minimizing measures. This doctoral work was supervised by two prominent mathematicians: Luigi Ambrosio at the Scuola Normale Superiore di Pisa and Cédric Villani at the École normale supérieure de Lyon. The combination of Ambrosio's expertise in geometric measure theory and the calculus of variations with Villani's pioneering work in optimal transport theory provided Figalli with a uniquely broad and deep training in the mathematical tools that would define his career.

The relationship between Figalli and Villani became particularly notable in the mathematical community. At the 2018 International Congress of Mathematicians, when Figalli was announced as a Fields Medal recipient, Villani was visibly moved, having himself received the Fields Medal in 2010. The image of Villani's emotional reaction to his former student's recognition became one of the memorable moments of the ceremony.

Career

Early Academic Positions

Following the completion of his doctorate in 2007, Figalli moved quickly through a series of academic positions at leading European and American institutions. He held positions at the University of Nice Sophia Antipolis in France and at the École Polytechnique, also in France, gaining experience in the French mathematical tradition that had been central to his doctoral training.

Figalli's early career was marked by a peripatetic quality that would become characteristic of his professional life. As described in Quanta Magazine, Figalli was "rarely in one place for very long," moving between institutions and countries as his research expanded and his reputation grew. This mobility reflected both the international nature of contemporary mathematics and Figalli's own openness to new environments and collaborations.

University of Texas at Austin

A significant phase of Figalli's career was spent at the University of Texas at Austin, where he served as a professor of mathematics. The University of Texas later highlighted that much of the work recognized by the Fields Medal was connected to research Figalli conducted during his time in Austin. The university's College of Natural Sciences noted that Figalli's contributions were in "an area of mathematical analysis known as optimal transport," and that his tenure at UT Austin was a productive period for the development of his most influential results.

During his years in Austin, Figalli established himself as one of the leading figures in the study of optimal transport and its connections to partial differential equations, probability theory, and geometric analysis. His research output during this period included significant papers that advanced the mathematical understanding of the Monge-Ampère equation, regularity theory, and stability problems.

ETH Zurich

In 2016, Figalli moved to ETH Zurich in Switzerland, where he took up a professorship in mathematics. ETH Zurich, one of the world's foremost institutions for science and technology, provided Figalli with an environment that supported his expanding research program. The move to Zurich also placed Figalli at the center of the European mathematical community, facilitating collaborations and interactions with a broad network of researchers.

At ETH Zurich, Figalli continued to develop his work on optimal transport while branching into new areas of application and theory. The announcement of his Fields Medal in August 2018 specifically noted his position at ETH Zurich, and the university publicly celebrated the recognition as a reflection of the strength of its mathematics department.

As of 2025, Figalli remains a professor at ETH Zurich, where his research group continues to work on problems at the intersection of optimal transport, partial differential equations, and geometric analysis.

Research

Figalli's research centers on the calculus of variations, partial differential equations, and optimal transport theory. Optimal transport, originally formulated by Gaspard Monge in the 18th century and later developed by Leonid Kantorovich, concerns the problem of finding the most efficient way to move a distribution of mass from one configuration to another. Figalli has made fundamental contributions to this field and its applications across mathematics.

According to reporting by The New York Times in 2025, Figalli's work on optimal transport has ranged across diverse applications, from understanding "the movements of clouds to the workings of chatbots." This breadth of application reflects the versatility of optimal transport as a mathematical framework and Figalli's ability to identify connections between abstract theory and concrete problems.

Quanta Magazine described Figalli's work as having "established the stability of everything from crystals to weather," highlighting the way in which his research provides rigorous mathematical foundations for understanding physical phenomena. In particular, Figalli has worked on stability results for geometric and functional inequalities, addressing questions about whether optimal shapes (such as the shapes of crystals) remain close to their ideal forms when subjected to small perturbations.

A central thread in Figalli's research has been the study of the Monge-Ampère equation, a nonlinear partial differential equation that arises naturally in optimal transport theory. His contributions to the regularity theory of solutions to this equation — that is, understanding how smooth or well-behaved solutions can be — have been particularly influential.

Figalli has also made important contributions to problems involving free boundary problems, the study of the Boltzmann equation in kinetic theory, and questions related to geometric measure theory. His doctoral thesis on optimal transportation and action-minimizing measures laid the groundwork for a research program that has consistently sought to unify different branches of analysis and geometry through the lens of optimal transport.

The Fields Medal citation recognized Figalli's "contributions to the theory of optimal transport, and its application to partial differential equations, metric geometry, and probability." The ETH Zurich announcement noted that the award recognized his "outstanding contribution to mathematical research."

The ERC, which had awarded Figalli a research grant in 2016, emphasized that Figalli's work exemplified the kind of frontier research that the council was established to support. The council highlighted his Fields Medal as evidence of the impact of European investment in fundamental research.

Figalli's research has also been published in leading mathematical journals. His work appears in venues such as Inventiones Mathematicae, among other top-tier publications.

Personal Life

Figalli has been noted for his itinerant lifestyle, moving frequently between countries and institutions throughout his career. Quanta Magazine characterized him as "a traveler who finds stability in the natural world," drawing a parallel between his nomadic professional life and his mathematical work on stability problems. His career has taken him from Italy to France, the United States, and Switzerland, and he has maintained connections to mathematical communities across all of these countries.

In his interview with the ERC, Figalli reflected on his personal journey into mathematics, noting that his childhood self had no awareness that a career as a mathematician was possible. This experience has informed his perspective on mathematical outreach and the importance of exposing young people to the breadth of careers available in the mathematical sciences.

Figalli holds Italian citizenship and has been based in Zurich, Switzerland, since joining ETH Zurich in 2016.

Recognition

Figalli has received numerous awards and honors throughout his career, reflecting the significance of his contributions to mathematics.

In 2012, Figalli was awarded the Peccot-Vimont Prize and delivered the Peccot Lectures at the Collège de France, a distinction given to young mathematicians in France for outstanding research. In the same year, he received the EMS Prize from the European Mathematical Society, which is awarded every four years to young mathematicians whose research has had a significant impact on the discipline.

In 2014, Figalli was an invited speaker at the International Congress of Mathematicians (ICM) held in Seoul, South Korea, a significant recognition of his standing in the international mathematical community.

In 2015, Figalli was awarded the Stampacchia Medal by the Italian Mathematical Union (Unione Matematica Italiana) for his contributions to the calculus of variations and partial differential equations.

In 2016, Figalli received a European Research Council (ERC) grant to support his research program, providing significant funding for his work at ETH Zurich.

In 2017, he was awarded the Feltrinelli Prize by the Accademia dei Lincei, one of Italy's most prestigious scientific honors.

The culmination of these recognitions came in August 2018, when Figalli was awarded the Fields Medal at the International Congress of Mathematicians in Rio de Janeiro, Brazil. The Fields Medal, awarded every four years to mathematicians under the age of 40, is considered the most prestigious award in mathematics. Figalli was 34 years old at the time.

Following the Fields Medal, Figalli received honorary doctorates (Doctorate Honoris Causa) from the Université Côte d'Azur in 2018 and the Polytechnic University of Catalonia in 2019, recognizing his contributions to mathematical research and his connections to the French and international academic communities.

Legacy

Figalli's contributions to the theory of optimal transport and partial differential equations have had a substantial impact on several areas of mathematics and its applications. His work has helped transform optimal transport from a somewhat specialized topic into a central framework connecting analysis, geometry, and probability. The breadth of applications that his research has touched — from the geometry of crystals to the mathematical modeling of atmospheric phenomena — illustrates the unifying power of the tools he has developed and refined.

The relationship between Figalli and his doctoral advisors, particularly Cédric Villani, represents a notable lineage in the study of optimal transport. Villani's own Fields Medal in 2010 recognized contributions to the same broad field, and the fact that both advisor and student received the Fields Medal within eight years underscores the centrality of optimal transport to contemporary mathematics. Figalli has continued to develop the field beyond the contributions of his predecessors, extending regularity results and stability analyses that have opened new avenues for research.

As a professor at ETH Zurich, Figalli has also contributed to the training of a new generation of mathematicians. His doctoral students and collaborators have worked on problems spanning the calculus of variations, free boundary problems, and geometric analysis, extending the reach of his research program.

Figalli's career also serves as an example of the international character of modern mathematical research. His trajectory from Rome to Pisa, Lyon, Nice, Paris, Austin, and Zurich reflects the global networks that sustain advanced mathematical inquiry. His remark about not knowing as a child that mathematicians existed has resonated in discussions about mathematical education and outreach, highlighting the importance of making career paths in mathematics visible to young people.

In the broader context of Italian mathematics, Figalli's Fields Medal represented a significant milestone. The recognition placed him in the company of the small number of Italian mathematicians who have received the award, reinforcing Italy's historical contributions to analysis and geometry.

As reported by The New York Times in 2025, Figalli's work continues to evolve, with applications of optimal transport extending into new domains, including connections to machine learning and artificial intelligence. His ongoing research suggests that the mathematical tools he has helped develop will continue to find relevance in both pure and applied settings for years to come.