2005-2006 seminars

We provide calculations of growth and spectra of Cayley and Schreier graphs related to some branch groups. Among the examples, we present a class of groups of intermediate growth defined by primitive polynomials over finite fields (the original...

Random covers of graphs, and random group actions on rooted trees, are different languages, that describe the same phenomenon. The former were studied by Amit, Linial. Matousek, Bilu. The latter were studied by Abert and Virag. Let T(n) be a binary...

Let $\alpha$ be an automorphism of a totally disconnected locally compact group $G$. There is a canonical form for $\alpha$ that partially fills the role played by the Jordan canonical form of $\mathrm{ad}( \alpha )$ in the case when $G$ is a Lie...

Let $G$ be a graph with maximum degree $\Delta$ whose vertex set is partitioned into $r$ parts $V(G)=V_1 \cup \ldots \cup V_r$. An independent transversal is an independent set in $G$ which contains exactly one vertex from each $V_i$. The problem of...

A Hamilton cycle in a graph G is a cycle passing through all vertices of G. Hamiltonicity is one of the most central and appealing notions in Graph Theory, with a variety of known conditions and approaches to show the existence of a Hamilton cycle...

I will explain a very intriguing connection between low dimensional topology, knot invariants, and quantum computation: It turns out that in some well defined sense, quantum computation is _equivalent_ to certain approximations of the Jones...

Studying the covolume of lattices goes back to the work of Siegel in the forties where he shows that $(2,3,7)$-triangular group is a lattice of minimum covolume in $G = \mathrm{SL}_2(\mathbb R)$. The case of $\mathrm{SL}_2(\mathbb C)$ has been open...

The main purpose of the talk is to describe an approach for the estimate of averages over orbits of certain functions on the space of lattices. These estimates play a crucial role in the study of the distribution of values at integral points of...

In this talk I will prove the following counterpoint to a result by Kashin and Szarek (cf. Theorem 1, C. R. Acad. Sci. Paris, Ser. I, 1336 (2003) 931-936)): There exists a map \phi from infinite-dimensional euclidean space into the space of...