Matthew Conder

Description

Title: Discrete and free two-generated subgroups of SL2

Abstract: It is well known that the Ping Pong Lemma can be applied to many two-generated subgroups of SL(2,R) (using the action by Möbius transformations on the hyperbolic plane) in order to determine properties such as freeness and/or discreteness. In particular, there is a practical algorithm (of Eick, Kirschmer and Leedham-Green) which, given any two elements of SL(2,R), will determine after finitely many steps whether or not the subgroup generated by these elements is both discrete and free of rank two. In this talk, I will show that a similar algorithm exists for two-generated subgroups of SL(2,K), where K is a non-archimedean local field (for instance, the p-adic numbers). Such groups act by isometries on a Bruhat-Tits tree, and the algorithm proceeds by computing and comparing various translation lengths, in order to determine whether or not a given two-generated subgroup of SL(2,K) is both discrete and free.

Period	2 Mar 2020
Visiting from	University of Cambridge (United Kingdom)
Visitor degree	PhD
Degree of Recognition	Local