Date & Time: Tuesday, 30th August, 2011 :: 2.00-3.15 PM

Venue: Ramanujan Hall

Title: Periods of quaternionic Shimura varieties

Speaker: Prof. Kartik Prasanna, University of Michigan, Ann Arbor

Abstract: A conjecture of Shimura (dating back to the early 80's) predicts relations between periods of arithmetic automorphic forms on quaternion algebras over totally real fields, up to algebraic factors. This conjecture was mostly proved by Michael Harris a few years later. I will first motivate and describe an integral refinement of Shimura's conjecture i.e. up to p-adic units for a good prime p. Then I will describe some work in progress (joint with Atsushi Ichino) on this more precise conjecture.