Vincent Pilloni is a French mathematician, specializing in

arithmetic geometry In mathematics, arithmetic geometry is roughly the application of techniques from algebraic geometry to problems in number theory. Arithmetic geometry is centered around Diophantine geometry, the study of rational points of algebraic varieties. ...

and the

Langlands program In mathematics, the Langlands program is a set of conjectures about connections between number theory, the theory of automorphic forms, and geometry. It was proposed by . It seeks to relate the structure of Galois groups in algebraic number t ...

Career

Pilloni studied at the

École Normale Supérieure École or Ecole may refer to: * an elementary school in the French educational stages normally followed by Secondary education in France, secondary education establishments (collège and lycée) * École (river), a tributary of the Seine flowing i ...

and received his doctorate in 2009 from

Université Sorbonne Paris Nord Sorbonne Paris North University () is a public university based in Paris, France. It is one of the thirteen universities that succeeded the University of Paris in 1968. It is a multidisciplinary university located in north of Paris, in the munici ...

with thesis advisor Jacques Tilouine and thesis ''Arithmétique des variétés de Siegel''. His research deals with, among other topics, the question of how the

modularity theorem In number theory, the modularity theorem states that elliptic curves over the field of rational numbers are related to modular forms in a particular way. Andrew Wiles and Richard Taylor proved the modularity theorem for semistable elliptic c ...

for

elliptic curve In mathematics, an elliptic curve is a smooth, projective, algebraic curve of genus one, on which there is a specified point . An elliptic curve is defined over a field and describes points in , the Cartesian product of with itself. If the ...

s over the rational numbers (which led to the proof of

Fermat's Last Theorem In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive number, positive integers , , and satisfy the equation for any integer value of greater than . The cases ...

) can be extended to

abelian varieties In mathematics, particularly in algebraic geometry, complex analysis and algebraic number theory, an abelian variety is a smooth projective algebraic variety that is also an algebraic group, i.e., has a group law that can be defined by regular f ...

. With George Boxer,

Frank Calegari Francesco Damien "Frank" Calegari is a professor of mathematics at the University of Chicago working in number theory and the Langlands program. Early life and education Frank Calegari was born on December 15, 1975. He has both Australian and A ...

and Toby Gee, he proved that all abelian surfaces and genus two curves over totally real fields are potentially modular and satisfy the Hasse-Weil conjecture. Pilloni is a '' Chargé de recherche'' of

CNRS 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 eng ...

Paris-Saclay University Paris-Saclay University (, ) is a combined technological research institute and public research university in Orsay, France. Paris-Saclay was established in 2019 after the merger of four technical ''grandes écoles,'' as well as several technol ...

based at the Institut de mathématique d'Orsay. In 2018 he was an invited speaker, with Fabrizio Andreatta and Adrian Iovita, at the

International Congress of Mathematicians The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU). The Fields Medals, the IMU Abacus Medal (known before ...

in Rio de Janeiro. In 2018 Pilloni received the Prix Élie Cartan. In 2021 he was awarded the

Fermat Prize The Fermat prize of mathematics, mathematical research biennially rewards research works in fields where the contributions of Pierre de Fermat have been decisive: * Statements of variational principles * Foundations of probability and analytic geo ...

Selected publications

* * * * * * * * with Benoit Stroh
Surconvergence, ramification et modularité
Astérisque, vol. 382, 2016, pp. 195–266. MR *

References

External links

website at ENS Lyon

Interview 2018, CNRS
(in French) * * * {{DEFAULTSORT:Pilloni, Vincent 21st-century French mathematicians Algebraic geometers École Normale Supérieure alumni University of Paris alumni Living people Year of birth missing (living people)