Title: On the Ramanujan conjecture for automorphic forms over function fields Speaker: Nicolas Templier (Cornell University) Time: 2018-6-6, 16:30-17:30 Place: N913 Abstract: Let G be a reductive group over a function field of large enough characteristic. We prove the temperedness at unramified places of automorphic representations of G, subject to a local assumption at one place, stronger than supercuspidality. Such an assumption is necessary, as was first shown by Saito-Kurokawa and Howe-Piatetskii-Shapiro in the 70's. Our method relies on the l-adic geometry of Bun_G, and on trace formulas. Work with Will Sawin. Attachment: