**SEMINARIO DE TEORIA DE GRUPOS UAM-ICMAT **

** Martes 28 de Febrero, a las 14:30 en el Aula 520, Modulo 1, UAM.**

** Speaker: Motiejus Valiunas (U. Southampton)**

** Title: Degree of commutativity of infinite groups**

** Abstract: For a finite group F, its degree of commutativity is defined to be the probability that two elements of F chosen at random commute. This has recently been defined for finitely generated infinite groups G by considering balls in G (of some radius n), i.e. finite sets of elements in G that are ``within distance n to the identity''. Degree of commutativity for infinite groups seems to depend on the rate of growth of these balls; in particular, it has been conjectured that many groups, namely all groups of exponential growth, have degree of commutativity zero. In the talk I will try to outline the construction and explain why degree of commutativity has to be zero for two particular classes of groups of exponential growth. For one of these classes an additional result is obtained, giving some insight into ``fine-counting'' of elements of groups with well-behaved growth.**

--