Date & Time: Wednesday, November 13, 2013, 16:00-17:00.
Venue: Ramanujan Hall
Speaker: Eknath Ghate, TIFR Mumbai
Title: Reductions of Galois Representations via the mod p LLC
Abstract: Breuil initiated the study of the mod p Local Langlands Correspondence (LLC), in two remarkable papers about a decade ago. Since then much progress has been made and many issues have been clarified, by Breuil, Berger, Colmez, Paskunas and others. In this talk we show how the LLC can be harnessed to describe the local behaviour of the reductions of certain two-dimensional p-adic Galois representations, for weights larger than 2p+1 and slopes between 1 and 2. This extends some recent results due to Buzzard-Gee, who dealt with slopes between 0 and 1.
This talk will be a slightly advanced talk, but we will try and gear it to a general colloquium audience. The material is from recent joint work with Abhik Ganguli.