Previous Special Year Seminar

Let $G$ be a simple $G(\mathbf Q)$-group of $G(\mathbf Q)$-rank at least 2. In 1987 T. N. Venkataramana showed that if $\Gamma \subset G(\mathbf Z)$ is an infinite subgroup whose commensurator is a subgroup of finite index in $G(\mathbf Z)$, then $...

A pair (G,H), where G is a group and H a subgroup, has relative Property T if every isometric action of G on a Hilbert space has a H-fixed point. In a connected Lie group or a lattice G, we characterize subgroups H such that (G,H) has relative...

The remarkable phenomenon of Superrigidity, discovered by Margulis in the context of linear representations of lattices in higher rank semi-simple groups, has motivated and inspired a lot of research on other "higher rank" groups and representations...

We analyze volume-preserving actions of product groups on Riemannian manifolds. Under a natural spectral irreducibility assumption, we prove the following dichotomy: Either the action is measurably isometric, in which case there are at most two...

In previous work we showed that arithmetic hyperbolic 2-manifolds that are isospectral are commensurable. In this talk we discuss the proof of the generalization to dimension 3. We had previously shown that if arithmetic hyperbolic 3-manifolds are...

In this talk I will give an overview of joint work with M. Rapoport and T. Yang on the construction of generating series whose coefficients are the classes of special divisors and 0-cycles on the arithmetic surfaces attached to Shimura curves. These...

We obtain asymptotic lower bounds for the spectral function of the Laplacian and for the remainder in local Weyl's law on compact manifolds. In the negatively curved case, thermodynamic formalism is applied to improve the estimates. Our results can...

We prove that if a Cartesian product of alternating groups is topologically finitely generated, then it is the profinite completion of a finitely Generated residually finite group. The same holds for Cartesian products of other simple groups under...

This talk is about joint work with A. Lubotzky. Let $F_n$ be the free group on $n\ge 2$ elements and $\A(F_n)$ its group of automorphisms. We have contructed new linear representations of $\A(F_n)$ arising through the action of finite index...