Seminars Sorted by Series

Ramanujan graphs are grphs with optimal bounds on their eigenvalues. They play an important role in combinatorics and computer science. Their constructions in the late 80's used the work of Deligne and Drinfeld proving the Ramanujan conjecture for...

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...

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...

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...

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...

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

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...

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...

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...

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...

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...

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...

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...

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...

A finitely generated group is called a Golod-Shafarevich group if it has a presentation with the following property: There exists a prime number p and a real number 0

We will discuss the following very recent result: Theorem. Let R be any finitely generated associative (not necessarily commutative) ring, with 1. Then for any n > stable range rank of the ring R, the group EL_n(R) has Kazhdan's property (T). The...

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...

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...

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...

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...

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...

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 $...

In joint work with Yehuda Shalom, we have proved Margulis' Normal Subgroup Theorem for any discrete subgroup $\Gamma$ of the automorphism group of a locally finite $A_2$-tilde building, $B$, provided that the quotient of $B$ by $\Gamma$ is compact...