Two-generator subgroups of SL2 over local fields

Abstract: In this talk, we will give an overview of some results and open problems relating to two-generator subgroups of SL2 over a local field K. We first consider the archimedean setting, where certain discrete and/or free two-generator subgroups of SL(2,R) and SL(2,C) can be identified by investigating their respective actions by Möbius transformations on the upper half plane and Riemann sphere. We then outline some recent results in the non-archimedean setting, obtained by studying the analogous action of SL(2,K) by isometries on the corresponding Bruhat-Tits tree. Finally, we discuss an application of this work to the problem of deciding whether a two-generator subgroup of SL(2,K) is dense.

group theory

Audience: researchers in the discipline

Symmetry in Newcastle