16:00
Eigenvarieties and p-adic rigidity for GSp4
Abstract
There has been substantial progress in the construction of eigenvarieties and $p$-adic families of automorphic forms, and their relationship with Selmer groups and ($p$-adic) $L$-functions. In this talk I will introduce some of these constructions, starting with modular forms, and the concept of complete $p$-adic rigidity: the non-existence of nontrivial $p$-adic deformations. I will explain some of the techniques used to study the geometry of eigenvarieties, and how these specialise to show that certain noncuspidal 'Saito—Kurokawa' points are completely $p$-adically rigid. If time permits, I will also briefly outline how similar strategies may be used to construct $p$-adic families through cuspidal, nonholomorphic Saito—Kurokawa points and to produce nontrivial Selmer classes predicted by the Bloch—Kato conjecture.
As you may know, the MSc in Mathematical Sciences (OMMS) is a standalone MSc which runs parallel with Part C. To help the MSc students feel welcomed to the department, we have a buddy system where our OMMS students are paired with current Part B students who will be staying on to Part C and they can communicate over the summer if they choose. A buddy would be someone the MSc student could ask informal questions (a bit like a college parent). MSc students and buddies would then be free to decide when to meet during the academic year.
Nominations are now open to recognise staff and students in MPLS who have gone above and beyond in their efforts to advance Equality, Diversity and Inclusion
That Robin Wilson, he doesn't half go on.
To infinity in fact, the topic of Robin's eighteenth and final talk on the equations that made mathematics. With an irritating little paradox to whet your appetite below and the full talk here.