Previous Special Year Seminar

We will present combinatorial approaches to property (T), spectra of graphs and Kazhdan constants.

Ideal classes in (totally real) number fields give naturally rise to compact orbits inside SL(n,Z)\SL(n,R) for the diagonal subgroup. We will discuss their (equi-)distribution properties as the field varies, and the two main ideas in our approach...

For a discrete group G and a finite subset X of G, let K(G, X) denote the Kazhdan constant of G associated to X. We define the uniform Kazhdan constant of G by K(G) = min { K(G,X) | X is finite and generates G }. Obviously K(G)>0 for any finite...

The talk will be introductory. We will first explain what Kac-Moody groups are. These groups are defined by generators and relations, but they are better understood via their actions on buildings. The involved class of buildings is interesting since...

Consider an affine building of type $A_n$-tilde, which is a simplicial compex of dimension $n$. For $n=1$, this is a tree, which we will require to be homogeneous. Consider the space of complex valued functions on the vertices of the building, and...

We will describe some recent ergodic theorems for general families of averages on semisimple Lie groups, and explain how they can be used to 1) Solve the lattice point counting problem for general domains in the group, with explicit estimate of the...

Consider an affine building of type $A_n$-tilde, which is a simplicial compex of dimension $n$. For $n=1$, this is a tree, which we will require to be homogeneous. Consider the space of complex valued functions on the vertices of the building, and...

I will explain a conjectural generalisation of Ihara's lemma in the theory of modular forms to higher dimensional automorphic forms and sketch how this conjecture implies the Sato-Tate conjecture for rational elliptic curves with somewhere...