3 1 Ja n 20 07 The rank gradient from a combinatorial viewpoint

The rank gradient from a combinatorial viewpoint

This paper investigates the asymptotic behaviour of the minimal number of generators of finite index subgroups in residually finite groups. We analyze three natural classes of groups: amenable groups, groups possessing an infinite soluble normal subgroup and virtually free groups. As a tool for the amenable case we generalize Lackenby’s trichotomy theorem on finitely presented groups.

3 1 Ja n 20 07 A COMBINATORIAL METHOD FOR CALCULATING THE MOMENTS OF LÉVY AREA

We present a new way to compute the moments of the Lévy area of a two-dimensional Brownian motion. Our approach uses iterated integrals and combinatorial arguments involving the shuffle product.

A ] 3 1 Ja n 20 05 K - Bessel functions associated to 3 - rank

Using Bessel-Muirhead system, we can express the K-bessel function defined on a Jordan algebra as linear combination of the J-solutions. We determine explicitly the coefficients when the rank of this Jordan algebra is three after a reduction to the rank two. The main tools are some algebraic identities developed for the occasion.

2 7 Ja n 20 04 Representations of trigonometric Cherednik algebras of rank 1 in positive characteristic Frédéric Latour

Ja n 20 06 UPPER BOUNDS FOR THE DAVENPORT CONSTANT

We prove that for all but a certain number of abelian groups of order n the Davenport constant is atmost n k +k−1 for positive integers k ≤ 7. For groups of rank three we improve on the existing bound involving the Alon-Dubiner constant.