Vincent Pilloni

Vincent Pilloni (born 1982) is a French mathematician, specializing in arithmetic algebraic geometry and the Langlands program.

Pilloni studied at the École Normale Supérieure and received his doctorate in 2009 from Paris 13 University with thesis advisor Jacques Tilouine and thesis Arithmétique des variétés de Siegel.[1][2]

His research deals with, among other topics, the question of how the modularity theorem for elliptic curves over the rational numbers (which led to the proof of Fermat's Last Theorem) can be extended to abelian varieties. With Fabrizio Andreatta and Adrian Iovita, he made significant progress on general modularity conjectures (following Fontaine-Mazur, Langlands, Clozel, and others).

Pilloni is a Chargé de recherche of CNRS at the École normale supérieure de Lyon (UMPA).

In 2018 he was an invited speaker, with Fabrizio Andreatta and Adrian Iovita, at the International Congress of Mathematicians in Rio de Janeiro.[3] In 2018 Pilloni received the Prix Élie Cartan.

Selected publications
  • Sur la théorie de Hida, Bull. Soc. Math. France, vol. 140, 2012, pp. 335–400.
  • Modularité, formes de Siegel et surfaces abéliennes, J. Reine Angew. Math., Vol. 666, 2012, pp. 35–82.
  • Prolongement analytique sur les variétés de Siegel, Duke Math. J., Vol. 157, 2011, pp. 167–222.
  • with Stéphane Bijakowski and Benoit Stroh: Classicité des formes modulaires superconvergentes, Annals of Mathematics, Vol. 183, 2016, pp. 975–1014
  • with Fabrizio Andreatta and Adrian Iovita: p-adic families of modular cusp forms, Annals of Mathematics, Vol. 181, 2015, pp. 623–697
  • with Andreatta and Iovita: Le Halo Spectral, Ann. Sci. ENS
  • with Andreatta and Iovita: On overconvergent Hilbert modular cusp forms, Astérisque, Vol. 382, 2016, pp. 163–193
  • with Benoit Stroh: Surconvergence, ramification et modularité, Astérisque, vol. 382, 2016, pp. 195–266. MR
  • Formes modulaires p-adiques de Hilbert de poids 1, Invent. Math., Vol. 208, 2017, pp. 633–676.
  • Higher coherent cohomology and p-adic modular forms of singular weight, 2017
    • For preprints, see Pilloni's website.

References
  1. Vincent Pilloni at the Mathematics Genealogy Project
  2. "Arithmétique des variétés de Siegel par Vincent Pilloni". theses.fr.
  3. Andreatta, Fabrizio; Iovita, Adrian; Pilloni, Vincent. "p-adic variation of automorphic sheaves" (PDF). Proc. Int. Long. of Math. – 2018 Rio de Janeiro. vol. 1. pp. 291–318.
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