2005-2006 seminars

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...

We introduce a metric space which is the closure of the isomorphism classes of graphs in a natural topology. It turns out that the regularity lemma is equivalent with the compactness of this space. We present applications, open questions, and...

Internal conflict is considered to be a fundamental psychological phenomenon, and many behaviors in both humans and animals have been attributed to it. However, from a biological standpoint, internal conflict is counterintuitive, in that it appears...

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...

Ramanujan complexes of type ${\tilde A}_n$ have been constructed by Lubotzky, Samuels and Vishne. In this talk I would like to propose a definition of Ramanujan complexes associated with buildings of any affine type. This involves defining...

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...

The Probabilistic Method is a powerful tool in tackling many problems in Combinatorics and it belongs to those areas of mathematical research that have experienced a most impressive growth in recent years. One of the parts of discrete mathematics...

Biological networks have so many possible states that exhaustive sampling is impossible. Successful analysis thus depends on simplifying hypotheses, but experiments on many systems hint that complicated, higher order interactions among large groups...

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

Coding theory emerged in the late 1940's, thanks to the works of Shannon and Hamming, as the theory supporting "reliable transmission of information (in the presence (fear?) of noise)". More than fifty years since, enormous progress has been made...