Seminars Sorted by Series

I intend to cover some basic questions and material regarding the phenomena in the cohomology of an arithmetic group "at infinity" when the corresponding locally symmetric space originating with an algebraic $k$-group $G$ of positive $k$-rank is non...

According to Langlands, pure motives are related to a certain class of automorphic representations.Can one see mixed motives in the automorphic set-up? For examples, can one see periods of mixed motives in entirely automorphic terms? The goal of...

Let $H = G/K$ be a symmetric space and $X = \Gamma \backslash H$ its locally symmetric quotient. An important problem is to understand the cohomology of the space $X$ (or, more or less equivalent, cohomology of the group $\Gamma$). The idea is that...

In the lectures I will formulate a conjecture asserting that there is a hidden action of certain motivic cohomology groups on the cohomology of arithmetic groups. One can construct this action, tensored with $\mathbb C$, using differential forms...

In the lectures I will formulate a conjecture asserting that there is a hidden action of certain motivic cohomology groups on the cohomology of arithmetic groups. One can construct this action, tensored with $\mathbb C$, using differential forms...

In the lectures I will formulate a conjecture asserting that there is a hidden action of certain motivic cohomology groups on the cohomology of arithmetic groups. One can construct this action, tensored with $\mathbb C$, using differential forms...

According to Langlands, pure motives are related to a certain class of automorphic representations.Can one see mixed motives in the automorphic set-up? For examples, can one see periods of mixed motives in entirely automorphic terms? The goal of...

It is well known that an irreducible representation of a group $G$ over a field $k$ admits a universal deformation to a representation over a complete Noetherian local ring, provided that it is absolutely irreducible, i.e. remains irreducible after...

I will introduce a new paradigm for comparing relative trace formulas, in order to prove instances of (relative) functoriality and relations between periods of automorphic forms.More precisely, for a spherical variety $X=H\backslash G$ of rank one...

I will introduce a new paradigm for comparing relative trace formulas, in order to prove instances of (relative) functoriality and relations between periods of automorphic forms.More precisely, for a spherical variety $X=H\backslash G$ of rank one...

This will be an informal working group on aspects of microlocal analysis that are relevant to automorphic forms. We will try to study Archimedean zeta integrals (which are related to local L-functions) using tools from the geometric theory of...

In these lectures, we will explore what insight can be gained into the arithmetic of Galois representations in a given dimension through the geometry of a higher-dimensional locally symmetric space near a boundary component. The starting point for...

In these lectures, we will explore what insight can be gained into the arithmetic of Galois representations in a given dimension through the geometry of a higher-dimensional locally symmetric space near a boundary component. The starting point for...

I will give a brief introduction to spherical varieties. With a view towards understanding the geometry of the moment map, I'll talk about the local structure theorem for spherical varieties. More concretely, if X is a spherical G-variety and B a...

In these lectures, we will explore what insight can be gained into the arithmetic of Galois representations in a given dimension through the geometry of a higher-dimensional locally symmetric space near a boundary component. The starting point for...

We will discuss Knop's paper "The asymptotic behavior of invariant collective motion" which analyzes the moment map for a spherical variety and relates it to a Weyl group.

Conclusion of last week's talk (Michał); overview of where we are and discussion of relation with representation theory and L-functions (Yiannis).

I will explain an application of the geometric Satake correspondence (in its derived form due to Bezrukavnikov-Finkelberg) to the study of differential operators on $G$-spaces (for $G$ complex reductive) and its classical version, the study of...

Rankin-Selberg integrals provide factorization of certain period integrals into local counterparts. Other, more elusive, periods can be studied in principle by the relative trace formula and other methods.

Following Waldspurger, Ichino-Ikeda...

I will discuss Knop's paper generalizing Harish-Chandra's isomorphism for the center of the universal enveloping algebra to the setting of spherical varieties. Here the center is replaced by the algebra of invariant differential operators. The idea...

Rankin-Selberg integrals provide factorization of certain period integrals into local counterparts. Other, more elusive, periods can be studied in principle by the relative trace formula and other methods.

Following Waldspurger, Ichino-Ikeda...

I will talk about some global questions on the concentration properties of automorphic forms that seem to be a natural environment in which to examine the interplay between the geometry and spectrum of spherical varieties, L-functions, and...

(joint w. Ben Bakker) Period spaces are quotients of period domains by arithmetic groups that parametrize hodge structures. These are typically complex-analytic orbifolds, but in most cases cannot be equipped with an algebraic structure. As a...

The problem of bounding character twists of low-rank L-functions has been attacked using a variety techniques, including delta methods and analysis of period integral representations. I'll discuss this problem, emphasizing joint work with Roman...

I will talk about some global questions on the concentration properties of automorphic forms that seem to be a natural environment in which to examine the interplay between the geometry and spectrum of spherical varieties, L-functions, and...

I will discuss an approach to the subconvexity problem for L-functions based on period integral formulae and amplification. In particular, I will describe work in progress with Ruixiang Zhang that attempts to prove a subconvex bound for the central...

We will present an introduction to Arthur's trace formula from an analytic point of view. After recalling Arthur's regularization procedure, we will review the absolute convergence and continuity of the trace formula for a large natural class of...

An orbit method (or Kirillov method) on compact $p$-adic groups establishes a one-to-one correspondence between irreducible representations and coadjoint orbits of dual blobs. After briefly recalling Howe’s Kirillov theory, we discuss its...

An orbit method (or Kirillov method) on compact $p$-adic groups establishes a one-to-one correspondence between irreducible representations and coadjoint orbits of dual blobs. After briefly recalling Howe’s Kirillov theory, we discuss its...

I will consider the asymptotic behavior of Laplacian eigenfunctions on a locally symmetric compact manifold as the volume approaches infinity. I will formulate a precise conjecture "à la Berry" and will describe some partial results obtained with...