The crucial contribution by Lafforgue to solve this question is the construction of compactifications of certain moduli stacks of shtukas.

[2] In 2002 at the 24th International Congress of Mathematicians in Beijing, China, he received the Fields Medal together with Vladimir Voevodsky.

In 1994 he received his Ph.D. under the direction of Gérard Laumon in the Arithmetic and Algebraic Geometry team at the Université de Paris-Sud.

He was detached as permanent professor of mathematics at the Institut des Hautes Études Scientifiques (IHÉS) in Bures-sur-Yvette, France, in 2000-2021.

In 2005, he was forced to resign from the Haut conseil de l'éducation after he expressed these views in a private letter that he sent to Bruno Racine, president of the HCE, that later was made public.