|Workshop on Representation Theory and Analysis on Locally Symmetric Spaces|
|Topic:||Endoscopy and cohomology growth on unitary groups|
|Affiliation:||University of Wisconsin; Member, School of Mathematics|
|Date:||Friday, March 9|
|Time/Room:||1:30pm - 2:30pm/|
Abstract: One of the principles of the endoscopic classification is that if an automorphic representation of a classical group is non-tempered at any place, then it should arise as a transfer from an endoscopic subgroup. One also knows that any representation of a unitary group that contributes to the cohomology of the associated symmetric space outside of middle degree must be non-tempered at infinity. By combining these two ideas, I will derive conjecturally sharp upper bounds for the growth of Betti numbers in congruence towers of complex hyperbolic manifolds. This is joint work with Sug Woo Shin.