Will Sawin (Columbia)
Ramanujan and the Other Geometry

Abstract: There are two main geometric approaches to automorphic forms over function fields, both due to Drinfeld. One approach, using moduli spaces of shtukas, was used by L. Lafforgue to prove the Langlands correspondence for GL_n and a number of consequences, including the Ramanujan conjecture for GL_n. The other approach, using moduli spaces of G-bundles, is the starting point of the geometric Langlands program. I will explain how it is (probably) possible to prove the Ramanujan conjecture for some automorphic forms on general reductive groups by the second geometric approach. This is joint work with Nicolas Templier.