Yesterday I went down to the Institute in Princeton with my friend Oisin McGuinness to attend one day of a conference in honor of Pierre Deligne that is going on there this week. Deligne has spent most of his career at the IHES and at the Institute, and this conference was in honor of his 61st birthday (I suspect they initially planned it for last year, but it got pushed back).
Deligne worked with Grothendieck at the IHES during the late sixties, and is perhaps best known for his proof of the Weil conjectures completed in 1974, an achievement which won him a Fields medal in 1978. The Weil conjectures motivated much of the work by Grothendieck and others in algebraic geometry during the fifties and sixties, and Deligne was able to finish a proof using Grothendieck’s machinery as well as some different ideas of his own. For more about Grothendieck, visit the Grothendieck Circle web-site. Grothendieck left the IHES around 1970, and later became a recluse, increasingly hostile towards his former colleagues, especially Deligne, who he attacked in his long unpublished manuscript “Recoltes et Semailles.” Several people told me that at the conference banquet held Tuesday night, after an array of different speakers rose to praise Deligne, especially for his generosity with his ideas and help to others, Deligne himself spoke and said that he was only repaying the debt he owed to Grothendieck, who himself was famous for such generosity.
One of the conference talks I heard was by Gerard Laumon, who described some of his work with Ngo Bau Chau on the Fundamental Lemma. Various lecture notes on this subject are available here. Laumon emphasized the role of equivariant cohomology in the proof, a method pioneered by Goresky, Kottwitz and MacPherson. Equivariant cohomology techniques are also crucially behind much work on topological quantum field theory, although of course the context is quite different there.