Seminars Sorted by Series

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...

"Beyond endoscopy", broadly interpreted, is the idea that functoriality should be realized as a comparison between stable trace formulas. The nature of this comparison, however, remains completely unclear.Broadening our scope to include the relative...

"Beyond endoscopy", broadly interpreted, is the idea that functoriality should be realized as a comparison between stable trace formulas. The nature of this comparison, however, remains completely unclear.Broadening our scope to include the relative...

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...

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...