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

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...

Abstract: Zywina showed that after passing to a suitable field extnesion, every abelian surface $A$ with real multiplication over some number field has geometrically simple reduction modulo $\frak{p}$ for a density one set of primes $\frak{p}$. One...

Abstract: In his classical work, Mazur considers the Eisenstein ideal $I$ of the Hecke algebra $\mathbb{T}$ acting on cusp forms of weight $2$ and level $\Gamma_0(N)$ where $N$ is prime. When $p$ is an Eisenstein prime, i.e. $p$ divides the...

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...