Jean-Loup Waldspurger


Jean-Loup Waldspurger 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 groups. 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". J.-L. Waldspurger proved the Gross-Prasad conjecture for SO groups on a p-adic body. With C. Moeglin, he wrote two large volumes establishing the stable trace formula for twisted spaces.
Some recent publications are available on its website.

Awards

He won the 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.