Jean-Loup Waldspurger

Jean-Loup Waldspurger
Born	2 July 1953 (1953-07-02) (age 71) France
Nationality	French
Alma mater	École normale supérieure
Known for	Waldspurger formula Waldspurger's theorem
Awards	Silver Medal of CNRS Clay Research Award (2009) ICM Speaker (1983, 1994, 2014) Peccot Lecture (1982/1983)
Scientific career
Fields	Mathematics

Jean-Loup Waldspurger (born 2 July 1953) is a French mathematician working on the Langlands program and related areas. He proved Waldspurger's theorem, the Waldspurger formula, and the local Gan–Gross–Prasad conjecture for orthogonal groups. He played a role in the proof of the fundamental lemma, reducing the conjecture to a version for Lie algebras. This formulation was ultimately proven by Ngô Bảo Châu.

Education

Waldspurger attained his doctorate at École normale supérieure in 1980, under supervision of Marie-France Vignéras.

Scientific work

J.-L. Waldspurger's work concerns the theory of automorphic forms. He highlighted the links between Fourier coefficients of modular shapes of half full weight and function values L or periods of modular shapes of full weight. With C. Moeglin, he demonstrated Jacquet's conjecture describing the discrete spectrum of the GL(n) groups.[1] Other works are devoted to orbital integrals on p-adic groups: unipotent orbital integrals, proof of the conjecture of Langlands-Shelstad transfer conditional on the "fundamental lemma" (which was later proved by Ngo-Bao-Chau[2]). J.-L. Waldspurger proved the Gross-Prasad conjecture for SO(N) groups on a p-adic field. With C. Moeglin, he wrote two large volumes establishing the stable trace formula for twisted spaces.[3]

Some recent publications are available on its website.[4]

Awards

He won the Mergier–Bourdeix Prize [fr] of the French Academy of Sciences in 1996. He was awarded the 2009 Clay Research Award for his results in p-adic harmonic analysis. He was elected as a member of French Academy of Sciences in 2017.[5]

References

1. Mœglin, C.; Waldspurger, J.-L. (1989). "Le spectre résiduel de ${\displaystyle {\rm {GL}}(n)}$". Annales scientifiques de l'École normale supérieure. 22 (4). Societe Mathematique de France: 605–674. doi:10.24033/asens.1595. ISSN 0012-9593.
2. Ngô, Bao Châu (23 April 2010). "Le lemme fondamental pour les algèbres de Lie". Publications mathématiques de l'IHÉS (in French). 111 (1). Springer Science and Business Media LLC: 1–169. arXiv:0801.0446. doi:10.1007/s10240-010-0026-7. ISSN 0073-8301. S2CID 118103635.
3. Moeglin, Colette; Waldspurger, Jean-Loup (2016). Stabilisation de la formule des traces tordue. Volume 1 (in French). Cham. ISBN 978-3-319-30049-8. OCLC 965778158.
4. "Publications". Archived from the original on 2020-08-09. Retrieved 2019-09-05.
5. "DIX-HUIT NOUVEAUX MEMBRES ÉLUS A L'ACADÉMIE DES SCIENCES" (PDF). 6 December 2017. Archived (PDF) from the original on 20 November 2021. Retrieved 10 December 2017.

• Jean-Loup Waldspurger, Mathématicien (in French)