Abstract: After discussing the notion of temperedness arising in the geometric Langlands program, I’ll sketch a proof of a version of the Ramanujan conjecture in that setting. Essential ingredients for the definition and the proof are the derived Satake equivalence and the Deligne-Lusztig (or Alvis-Curtis) duality functors. I will then explain the role of the Ramanujan conjecture in the geometric Langlands program for the group SL_2.
Zoom link: https://yale.zoom.us/j/99305994163 [4], contact the organizers (Gurbir Dhillon and Junliang Shen) for the passcode.