# Vincent Lafforgue

Vincent Lafforgue
Born20 January 1974 (age 45)
NationalityFrench
EducationLycée Louis-le-Grand
Alma materÉcole normale supérieure
University of Paris
AwardsEMS Prize (2000)
CNRS Silver Medal (2015)
Breakthrough Prize in Mathematics (2019)
Scientific career
FieldsMathematics
InstitutionsUniversité Grenoble Alpes

Vincent Lafforgue (born 20 January 1974) is a French mathematician who is active in algebraic geometry, especially in the Langlands program,[1] and a CNRS "Directeur de Recherches" at the Institute Fourier in Grenoble. He is the younger brother of Fields Medalist Laurent Lafforgue.

## Awards

Lafforgue was awarded the 2000 EMS Prize for his contribution to the K-theory of operator algebras: the proof of the Baum–Connes conjecture for discrete co-compact subgroups of ${\displaystyle SL(3,\mathbb {R} )}$, ${\displaystyle SL(3,\mathbb {C} )}$, ${\displaystyle SL(3,\mathbb {Q} _{p})}$ and some other locally compact groups, and of more general objects. He participated in the International Mathematical Olympiad and wrote two perfect papers in 1990 and 1991, making him one of only two French mathematicians to win two gold medals (besides Joseph Najnudel, 1997–98).[2] Lafforgue was an Invited Speaker of the ICM in 2002 in Beijing, China [3] and a Plenary Speaker of the ICM in 2018 in Rio de Janeiro, Brazil.[4] He was awarded the 2019 Breakthrough Prize in Mathematics[5] for his "elegant and groundbreaking contributions to the Langlands program in the function field case", namely for establishing the Langlands Correspondence (the direction from automorphic forms to Galois representations) for connected reductive groups defined over global function fields.[6][7]

## References

1. ^ Shtukas for reductive groups and Langlands correspondence for function fields Vincent Lafforgue, March, 2017
2. ^
3. ^ V. Lafforgue (2002). "Banach KK-theory and the Baum-Connes Conjecture" (PDF). Proceedings of the International Congress of Mathematicians (Beijing, 2002). vol. II. Beijing: Higher Ed. Press. pp. 795–812.
4. ^ [http://www.icm2018.org/portal/program-at-a-glance.html, V. Lafforgue, "Shtukas for reductive groups and Langlands correspondence for function fields", arXiv:1803.03791, http://vlafforg.perso.math.cnrs.fr/files/cht-ICM-lafforgue.pdf
5. ^ Winners of the 2019 Breakthrough Prize in Mathematics Announced Irish Tech News, October 18, 2018
6. ^ V. Lafforgue (2018). "Chtoucas pour les groupes réductifs et paramétrisation de Langlands". Journal of the American Mathematical Society (2018). vol. 31. pp. 719–891.(arXiv:1209.5352)
7. ^ B. Stroh(2016), "La paramétrisation de Langlands globale sur les corps des fonctions (d'après Vincent Lafforgue)", Séminaire Bourbaki 68ème année, 2015-2016, no. 1110, Janvier 2016. (https://webusers.imj-prg.fr/~benoit.stroh/bourbaki.pdf)