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 field. With C. Moeglin, he wrote two large volumes establishing the stable trace formula for twisted spaces.Some recent publications are available on its website.