Alessio Figalli

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Alessio Figalli
Figalli in 2019
Alessio Figalli
Born4/2/1984
BirthplaceRome, Italy
NationalityItalian
OccupationMathematician
EmployerETH Zurich
Known forCalculus of variations, partial differential equations, optimal transport
EducationPhD in Mathematics (2007)
AwardsFields Medal (2018), EMS Prize (2012), Feltrinelli Prize (2017)
Websitehttps://people.math.ethz.ch/~afigalli/

Alessio Figalli (born 2 April 1984) is an Italian mathematician. His work spans the calculus of variations, partial differential equations, and optimal transport, placing him among the most recognized mathematicians of his generation. Born in Rome, he developed his talents through studies in Italy and France before launching an academic career across Europe and the United States. In 2018, he won the Fields Medal, often called the highest honor in mathematics, for contributions to optimal transport theory and its applications to partial differential equations, metric geometry, and probability.[1] His research has tackled everything from crystal stability to the mathematics of clouds and weather patterns.[2] Since 2016, he's held a professorship at ETH Zurich.

Early Life

Alessio Figalli was born on 2 April 1984 in Rome, Italy.[1] He didn't dream of becoming a mathematician as a kid. In an interview after his Fields Medal win, he recalled: "Growing up I didn't even know that mathematicians existed!"[3] His path into mathematics wasn't inevitable. It was something he discovered through school and exposure to the discipline.

His mathematical development took shape during formative years in Italy. According to Quanta Magazine, Figalli found his way to mathematics gradually, without the prodigy narrative that marks some Fields Medal winners. His interests sharpened as he encountered harder mathematical ideas. The Italian educational system, with its rigorous training in analysis and geometry, shaped his trajectory.[4]

Rome in those years offered him cultural and intellectual richness. His journey from the Italian capital to the peak of international mathematics reflects both the opportunities of the European academic system and his own deepening commitment to research.

Education

Figalli studied at the University of Pisa and the Scuola Normale Superiore di Pisa, two of Italy's finest institutions for mathematics and science. The Scuola Normale Superiore has long produced leading Italian mathematicians, and his time there gave him a thorough grounding in mathematical analysis.[5]

For his doctorate, he pursued a joint program between the Scuola Normale Superiore di Pisa and the École normale supérieure de Lyon in France. He finished his PhD in 2007. His thesis was titled Optimal transportation and action-minimizing measures.[6] Two prominent mathematicians supervised his work: Luigi Ambrosio at Pisa and Cédric Villani at Lyon.[1] Ambrosio brought expertise in geometric measure theory and the calculus of variations. Villani offered pioneering insights into optimal transport. That combination gave Figalli unusually broad and deep training in the tools that would define his career.

His relationship with Villani became especially significant in the mathematical world. At the 2018 International Congress of Mathematicians, when Figalli won the Fields Medal, Villani visibly reacted with emotion. He'd won the same prize in 2010. Their moment together became one of the ceremony's most memorable images.[7]

Career

Early Academic Positions

After finishing his doctorate in 2007, Figalli moved quickly through leading institutions across Europe and America. He worked at the University of Nice Sophia Antipolis in France and at the École Polytechnique, also in France, absorbing the French mathematical tradition that had shaped his doctoral training.[5]

Early on, he was rarely staying in one place. Quanta Magazine described him as "a traveler," moving between countries and institutions as his research expanded and reputation grew.[4] This reflected contemporary mathematics' international character and his own hunger for new environments and partnerships.

University of Texas at Austin

A major chapter of his career unfolded at the University of Texas at Austin, where he was a mathematics professor. Much of the work that earned his Fields Medal came from research he did there. The university's College of Natural Sciences noted that his contributions were in "optimal transport," an area of mathematical analysis, and that UT Austin was a productive base for developing his most influential results.[8]

During those years, he became a leading figure in optimal transport and its connections to partial differential equations, probability theory, and geometric analysis. He produced significant papers advancing mathematical understanding of the Monge-Ampère equation, regularity theory, and stability problems.

ETH Zurich

In 2016, Figalli joined ETH Zurich in Switzerland as a mathematics professor. One of the world's top science and technology schools, ETH provided an ideal setting for his expanding research. The move placed him at Europe's mathematical center, enabling collaborations with researchers across the continent.[1]

At Zurich, he developed his optimal transport work while exploring new applications and theory. When his Fields Medal was announced in August 2018, the news specifically noted his position at ETH Zurich, and the university celebrated it as a mark of its mathematics department's strength.[1]

He remains there as of 2025, leading a research group working on problems spanning optimal transport, partial differential equations, and geometric analysis.[2]

Research

His research focuses on the calculus of variations, partial differential equations, and optimal transport theory. Optimal transport was originally formulated by Gaspard Monge in the 18th century and later developed by Leonid Kantorovich. The core problem is 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 mathematical applications.[2]

The New York Times reported in 2025 that his work on optimal transport has ranged widely, from "the movements of clouds to the workings of chatbots."[2] This breadth shows optimal transport's versatility as a mathematical framework and Figalli's gift for spotting connections between abstract theory and real problems.

Quanta Magazine said his work "established the stability of everything from crystals to weather," highlighting how he provides rigorous mathematical foundations for understanding physical phenomena.[4] He's worked particularly on stability results for geometric and functional inequalities. Questions like whether optimal shapes, such as crystal forms, stay close to their ideal shapes when slightly disturbed.

The Monge-Ampère equation stands at the core of his research. This nonlinear partial differential equation arises naturally in optimal transport theory. His contributions to understanding solutions' regularity, that is how smooth and well-behaved they are, proved especially influential.

He's also made important contributions to free boundary problems, the Boltzmann equation in kinetic theory, and questions in geometric measure theory. His doctoral thesis laid groundwork for a research program consistently seeking to unify different branches of analysis and geometry through optimal transport's lens.[6]

The Fields Medal citation recognized his "contributions to the theory of optimal transport, and its application to partial differential equations, metric geometry, and probability."[1] ETH Zurich's announcement noted the award for his "outstanding contribution to mathematical research."[1]

The European Research Council, which gave him a research grant in 2016, emphasized that his work exemplified frontier research the council was created to back. They highlighted his Fields Medal as proof of European investment in fundamental research's impact.[9]

His research appears in leading mathematical journals. Works go to venues like Inventiones Mathematicae and other top publications.[10][11]

Personal Life

He's known for his itinerant lifestyle. Moving frequently between countries and institutions has been his way. Quanta Magazine called him "a traveler who finds stability in the natural world," drawing a parallel between his nomadic professional life and his mathematical work on stability problems.[4] His career has taken him from Italy to France, the United States, and Switzerland, maintaining ties across all these mathematical communities.

In his ERC interview, he reflected on his personal journey into mathematics. As a child, he didn't know a mathematician's career was even possible. This experience has shaped how he thinks about mathematical outreach and the importance of showing young people the range of careers available in mathematics.[3]

He holds Italian citizenship and has been based in Zurich, Switzerland, since 2016.

Recognition

His achievements have brought numerous awards and honors.

In 2012, Figalli received the Peccot-Vimont Prize and delivered the Peccot Lectures at the Collège de France, given to young French mathematicians for outstanding research. That same year, he won the EMS Prize from the European Mathematical Society, awarded every four years to young mathematicians whose work significantly impacts the discipline.[12]

He was an invited speaker at the International Congress of Mathematicians (ICM) in Seoul in 2014, a major recognition of his standing in the international mathematical community.[13]

In 2015, the Italian Mathematical Union gave him the Stampacchia Medal for his work in the calculus of variations and partial differential equations.[14]

A year later, he received a European Research Council (ERC) grant to back his research program at ETH Zurich.[9]

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

Then came August 2018. The International Congress of Mathematicians in Rio de Janeiro announced him as a Fields Medal winner. The Fields Medal, given every four years to mathematicians under 40, is mathematics' most prestigious award. Figalli was 34.[1][15]

Following the Fields Medal, he received honorary doctorates from the Université Côte d'Azur in 2018 and the Polytechnic University of Catalonia in 2019, recognizing his research and connections to French and international academia.

Legacy

His contributions to optimal transport theory and partial differential equations have deeply shaped several areas of mathematics and its applications. He's helped transform optimal transport from a specialized topic into a central framework connecting analysis, geometry, and probability. The range of applications his research touches, from crystal geometry to atmospheric modeling, shows the unifying power of the tools he's developed and refined.[4][2]

His relationship with his doctoral advisors, especially Cédric Villani, represents a notable lineage in optimal transport study. Villani won the Fields Medal in 2010 for the same broad field of work. Both advisor and student received the medal within eight years, underscoring optimal transport's centrality to modern mathematics. Figalli has pushed the field beyond his predecessors' contributions, extending regularity results and stability analyses that opened new research directions.[7]

As an ETH Zurich professor, he's also trained a new generation of mathematicians. His doctoral students and collaborators work on problems spanning the calculus of variations, free boundary problems, and geometric analysis, extending his research program's reach.[5]

His career shows modern mathematical research's international character. His path from Rome to Pisa, Lyon, Nice, Paris, Austin, and Zurich reflects the global networks that sustain advanced inquiry. His childhood comment about not knowing mathematicians existed has resonated in discussions about mathematical education and outreach. It highlights how vital it is to make mathematics careers visible to young people.[3]

For Italian mathematics, his Fields Medal was a milestone. It placed him among the small group of Italian mathematicians who've won the award, reinforcing Italy's historical role in analysis and geometry.

The New York Times reported in 2025 that his work keeps evolving, with optimal transport applications extending into new domains, including machine learning and artificial intelligence. His ongoing research suggests the mathematical tools he's helped create will remain relevant in pure and applied settings for years to come.[2]

References

  1. ↑ 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 "Alessio Figalli wins the "Nobel Prize of Mathematics"". 'ETH Zürich}'. 2018-08-01. Retrieved 2026-02-24.
  2. ↑ 2.0 2.1 2.2 2.3 2.4 2.5 "A Mathematician Who Makes the Best of Things".The New York Times.2025-02-14.https://www.nytimes.com/2025/02/14/science/mathematics-figalli-optimal-transport.html.Retrieved 2026-02-24.
  3. ↑ 3.0 3.1 3.2 "Growing up I didn't even know that mathematicians existed!". 'European Research Council}'. 2018-08-01. Retrieved 2026-02-24.
  4. ↑ 4.0 4.1 4.2 4.3 4.4 "A Traveler Who Finds Stability in the Natural World".Quanta Magazine.2018-08-01.https://www.quantamagazine.org/a-traveler-who-finds-stability-in-the-natural-world-20180801/.Retrieved 2026-02-24.
  5. ↑ 5.0 5.1 5.2 "Alessio Figalli — Homepage". 'ETH Zurich}'. Retrieved 2026-02-24.
  6. ↑ 6.0 6.1 "Optimal transportation and action-minimizing measures". 'ETH Zurich (personal page)}'. 2007. Retrieved 2026-02-24.
  7. ↑ 7.0 7.1 "[Weekend Math] Our Precious Mathematical Family".동아사이언스.2025-01.https://www.dongascience.com/en/news/41905.Retrieved 2026-02-24.
  8. ↑ "Fields Medal Recognition Linked to Work at UT Austin". 'The University of Texas at Austin}'. 2018-08-01. Retrieved 2026-02-24.
  9. ↑ 9.0 9.1 "ERC grantee receives 2018 Fields Medal for Mathematics". 'European Research Council}'. 2018-08-01. Retrieved 2026-02-24.
  10. ↑ "Figalli et al. (2010) — Inventiones Mathematicae". 'SAO/NASA Astrophysics Data System}'. 2010. Retrieved 2026-02-24.
  11. ↑ "De Philippis, Figalli (2013) — Inventiones Mathematicae". 'SAO/NASA Astrophysics Data System}'. 2013. Retrieved 2026-02-24.
  12. ↑ "6th European Congress of Mathematics — Prizes". '6th European Congress of Mathematics}'. 2012. Retrieved 2026-02-24.
  13. ↑ "ICM 2014 — Scientific Program Topics". 'ICM 2014}'. 2014. Retrieved 2026-02-24.
  14. ↑ "Motivazioni — Stampacchia Medal to Figalli". 'Unione Matematica Italiana}'. 2015. Retrieved 2026-02-24.
  15. ↑ "Alessio Figalli wins the 'Nobel Prize of Mathematics'".EurekAlert! Science News Releases.2018-08-01.https://www.eurekalert.org/news-releases/643572.Retrieved 2026-02-24.
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