Discrete 2-generator subgroups of PSL2(ℝ) have been extensively studied by investigating their action by Möbius transformations on the hyperbolic plane. Due to work of Gilman, Rosenberger, Purzitsky and many others, there is a complete classification of such groups by isomorphism type, and an algorithm to decide whether or not a 2-generator subgroup of PSL2(ℝ) is discrete.
Here we completely classify discrete 2-generator subgroups of PSL2(ℚp) over the p-adic numbers ℚp by studying their action by isometries on the corresponding Bruhat-Tits tree. We give an algorithm to decide whether or not a 2-generator subgroup of PSL2(ℚp) is discrete, and discuss how this can be used to decide whether or not a 2-generator subgroup of SL2(ℚp) is dense.
This is joint work with Jeroen Schillewaert.
This video was produced by the Sydney Mathematical Research Institute, as part of their SMRI seminar series.
