EVENT DETAILS AND ABSTRACT

Title: Counting non-tempered automorphic forms using endoscopy
Speaker: Mathilde Gerbelli-Gauthier
Speaker Info: McGill University
Brief Description:
Special Note:
Abstract:

How many automorphic representations of level n have a specified local factor at the infinite places? On SL_2, for nice enough representations, the question reduces to counting dimensions of spaces of modular forms, and is completely understood. More generally, when this local factor is a discrete series representation, this question is asymptotically well-understood as n grows. Non-tempered local factors, on the other hand, violate the Ramanujan conjecture and should be very rare. We use the endoscopic classification for representations to quantify this rarity in the case of cohomological representations of unitary groups, and discuss some applications to the growth of cohomology of Shimura varieties.