Speaker: Beth Romano (University of Cambridge)
Wild Ramification and the Local Langlands Correspondence
The local Langlands correspondence (LLC) is an amalgam of conjectures that has driven research in both representation theory and number theory for the past 50 years. In this talk, we will look at explicit examples to explore a particularly mysterious piece of the LLC, related to wild ramification.
More specifically, given a prime number p, the LLC predicts a way of understanding Galois extensions of the field of p-adic numbers. The part of the correspondence related to wildly ramified extensions seems to behave badly whenever p is too small. I will talk about progress in understanding and proving this part of the correspondence.
KdVI meeting room, room F3.20