Previous Special Year Seminar

Paley graphs are well-known combinatorial objects which have many interesting properties. Many of these properties come from their symmetry under the automorphisms x-->ax+b of the affine line over a finite field F with q elements (q=4m+1). We...

Given a higher rank arithmetic group (E.g. SL(3,Z)) it has r(n) complex irreducible representations of degree n. We will study the the rate of growth of r(n), the associated zeta function SUM(r(n)n^(-s)), its Euler factorisation etc. Some...

The classification of finite simple groups is widely acknowledged to be one of the major results in modern mathematics. The successful completion of its proof was announced in the early 1980's by Daniel Gorenstein. The original proof occupied...

Closed subgroups of the automorphism group of a tree which acts locally primitively have a rich structure theory. Combined with superrigidity for irreducible lattices in products of trees such that the projection in each factor is locally primitive...

I will discuss a proof of the fact that given a finite dimensional division algebra D over an arbitrary field, any finite quotient of the multiplicative group D^* is solvable (joint work with Y.Segev and G.Seitz). Time permitting, I will also talk...

We will show how self-similar groups H(k) generated by finite automata can be related to Hanoi Tower games on k=3,4,... pegs. Then we will consider the spectrum of a Schreier graph of Hanoi Group H(3), will show that the group is of branch type, and...

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