| Date | Speaker | Type | Topic |
|---|---|---|---|
| Aug 24 | Sug Woo Shin (Berkeley) | II | Introduction and organization (plan) |
| Aug 31 | Alex Carney (Berkeley) | II | Siegel modular varieties |
| Sept 7 | Dylan Yott (Berkeley) | II | Cohomology of locally symmetric spaces and automorphic forms |
| Sept 14 | Watson Ladd (Berkeley) | II | Main results on the global Langlands correspondence |
| Sept 21 | Sander Mack-Crane (Berkeley) | II | Borel-Serre compactification and reduction to liftability |
| Sept 26, 28, 30 | special seminar series: Ahmed Abbes, 3:40-5:00pm, 939 Evans Hall, Lifting the Cartier transform of Ogus-Vologodsky modulo p^n | ||
| Oct 5 | Joe Stahl (Berkeley) | II | Introduction to adic spaces |
| Oct 12 | Ravi Fernando (Berkeley) | II | Introduction to perfectoid spaces |
| Oct 19 | Eugenia Rosu (Berkeley) | I |
The Birch and Swinnerton-Dyer conjecture predicts that we have
non-torsion rational points on an elliptic curve iff the L-function
corresponding to the elliptic curve vanishes at 1. Thus BSD predicts
that a positive integer N is the sum of two cubes if L(E_N, 1)=0,
where L(E_N, s) is the L-function corresponding to the elliptic curve
E_N: x^3+y^3=N. We have computed several formulas that relate L(E_N,
1) to the trace of a modular function at a CM point. This offers a
criterion for when the integer N is the sum of two cubes. Furthermore,
when L(E_N, 1) is nonzero we get a formula for the number of elements
in the Tate-Shafarevich group.
Integers that can be written as the sum of two rational cubes (abstract) |
| Oct 26 | Alex Youcis (Berkeley) | II | Canonical subgroups with application to Siegel modular varieties |
| Nov 2 | Alexander Bertoloni Meli (Berkeley) | II | Hodge-Tate period morphism and perfectoid Gamma(p^infty)-level Siegel modular varieties, I |
| Nov 9 | Alex Youcis (Berkeley) | II | Hodge-Tate period morphism and perfectoid Gamma(p^infty)-level Siegel modular varieties, II |
| Nov 16 | Cheng-Chiang Tsai (MIT) | I |
Orbital integrals integrate test functions over conjugacy orbits of p-adic reductive groups. They appear in the Arthur-Selberg trace formula, which is fundamental to the study of automorphic representations. In this talk, we explain some modern aspects of orbital integrals by demonstrating the $GL_n$ case for which we deal with lattice countings and local compactified Jacobians. After that we discuss their asymptotic properties and present a result about uniform bounds on orbital integrals as an application.
Local compactified Jacobians, orbital integrals and uniform bounds (abstract) |
| Nov 23 | none | no talk | |
| Nov 30 | Jessica Fintzen (U of Michigan) | I |
Reeder and Yu gave recently a new construction of certain supercuspidal representations of p-adic reductive groups (called epipelagic representations). Their construction relies on the existence of stable vectors in the first Moy-Prasad filtration quotient under the action of a reductive quotient. We will explain these ingredients and present a theorem about the existence of such stable vectors for all primes p. This builds on a result of Reeder and Yu about the existence of stable vectors for large primes and generalizes the paper of the speaker and Romano, which treats the case of an absolutely simple split reductive group.
In addition, we will present a general set-up that allows us to compare the Moy-Prasad filtration representations for different primes p. This provides a tool to transfer results about the Moy-Prasad filtration from one prime to arbitrary primes and also yields new descriptions of the Moy-Prasad filtration representations.
On the Moy-Prasad filtration and supercuspidal representations (abstract) |
| Dec 7 | Eugenia Rosu (Berkeley) | II | Lifting mod p cohomology classes to Siegel cuspforms in char 0 |