Special Year 2017-18: Locally Symmetric Spaces: Analytical and Topological Aspects

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...

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...

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...

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...

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...

Abstract: We prove that the weight 4 Beilinson's regulator map can be expressed via the classical n-logarithms, $n \leq 4$. This plus Borel's theorem implies Zagier's conjecture, relating the value of the Dedekind zeta functions at $s=4$ and the...

Abstract: A rather notorious mistake occurs p. 217 in the proof of Lemma 6.3 of the book "Simple algebras, base change, and the advanced theory of the trace formula" (1989) by J. Arthur, L. Clozel. E. Lapid and J. Rogawski (1998) proposed a proof of...

Abstract: An important input into modularity lifting theorems is an understanding of the geometry of Galois deformation rings, especially local deformation rings with p-adic Hodge theory conditions at $\ell=p$. Outside of a few cases (ordinary...