Seminars Sorted by Series

The theory of (\varphi, \Gamma)-modules, which was introduced by Fontaine in the early 90's, classifies local Galois representations into modules over certain power series rings carrying certain extra structures (\varphi and \Gamma). In a recent...

We study families of filtered phi-modules associated to families of p-adic Galois representations as considered by Berger and Colmez. We show that the weakly admissible locus in a family of filtered phi-modules is open and that the groupoid of...

In this talk, I will explain my joint work with Junecue Suh on when and why the cohomology of Shimura varieties (with nontrivial integral coefficients) has no torsion, based on certain new vanishing theorems we have proved. (All conditions involved...

Iwasawa developed his theory for class groups in towers of cyclotomic fields partly in analogy with Weil's theory of curves over finite fields. In this talk, we present another such conjectural analogy. It seems intertwined with Leopoldt's...

To a regular algebraic cuspidal representation of GL(2) over a quadratic imaginary field, whose central character is conjugation invariant, Taylor et al. associated a two dimensional Galois representation which is unramified at l different from p...

Given a cuspidal automorphic representation of GL(n) which is regular algebraic and conjugate self-dual, one can associate to it a Galois representation. This Galois representation is known in most cases to be compatible with local Langlands. When n...

In this talk, I will describe a construction of a geometric realisation of a p-adic Jacquet-Langlands correspondence for certain forms of GL(2) over a totally real field. The construction makes use of the completed cohomology of Shimura curves, and...

These two talks will be about automorphic cohomology in the non-classical case. By definition, automorphic cohomology are the groups $H^q( \Gamma \backslash D, L)$ where $D$ is a homogeneous complex manifold $G_{\mathbb R}/H$, $G_{\mathbb R}$ is a...

These two talks will be about automorphic cohomology in the non-classical case. By definition, automorphic cohomology are the groups $H^q( \Gamma \backslash D, L)$ where $D$ is a homogeneous complex manifold $G_{\mathbb R}/H$, $G_{\mathbb R}$ is a...

Let G be a connected reductive group over Q such that G(R) has discrete series representations. I will report on some statistical results on the Satake parameters (w.r.t. Sato-Tate distributions) and low-lying zeros of L-functions for families of...

We attach Galois representations to automorphic representations on unitary groups whose weight (=component at infinity) is a holomorphic limit of discrete series. The main innovation is a new construction of congruences, using the Hasse Invariant...

I'll talk on work in progress on algebraic and analytic geometry over the field of one element F_1. This work originates in non-Archimedean analytic geometry as a result of a search for appropriate framework for so called skeletons of analytic...

Periods of automorphic forms over spherical subgroups tend to: (1) distinguish images of functorial lifts and (2) give information about L-functions. This raises the following questions, given a spherical variety X=H\G: Locally, which irreducible...

A well known result of Coleman says that p-adic overconvergent (ellitpic) eigenforms of small slope are actually classical modular forms. Now consider an overconvergent p-adic Hilbert eigenform F for a totally real field L. When p is totally split...

These two talks will be about automorphic cohomology in the non-classical case. By definition, automorphic cohomology are the groups $H^q( \Gamma \backslash D, L)$ where $D$ is a homogeneous complex manifold $G_{\mathbb R}/H$, $G_{\mathbb R}$ is a...

The Bernstein center plays a role in the representation theory of locally profinite groups analogous to that played by the center of the group ring in the representation theory of finite groups. When F is a finite extension of Q_p, we discuss the...

Suppose that G is a connected, quasisplit, orthogonal or symplectic group over a field F of characteristic 0. We shall describe a classification of the irreducible representations of G(F) if F is local, and the automorphic representations of G in...

We shall recall the spectral terms from the trace formula for G and its stabilaization, as well as corresponding terms from the twisted trace formula for GL(N). We shall then discuss aspects of the proof of the theorems stated in the first talk that...