Mathematics Colloquium Friday, 20 Oct. 4 pm ==================== Venue: Ramanujan Hall Host: Ravi Raghunathan Speaker: Dinakar Ramakrishnan Affiliation: California Institute of Technology Title: Abelian 3-folds of Picard type, and a uniform irreducibility result Abstract: Half a century ago Manin proved a uniform boundedness result for the p-power torsion of any non-CM elliptic curve E over a given number field k. A few years ago, Cadoret and Tamagawa established a similar result for the p-adic representations attached to 1-dimensional abelian families. In joint work with M. Dimitrov, we provide the 1st evidence in higher dimension, for families of abelian 3-folds parametrized by certain Picard modular _surfaces_. The proof also involves aspects of (global and local) representation theory.