**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.