Chabauty Limits of Subgroups in SL(n, Qp)

Given a second countable locally compact group, G, the set of all subgroups S(G) may be endowed with the Chabauty topology, under which it is a compact space. In general, it is difficult to understand the full topology of the space S(G), and the complete homeomorphism type is known only in very few cases. In the first part of the talk we will give an introduction to the Chabauty topology. Then we will study limits of different kinds of subgroups in SL(n, Qp) using the geometry of the Bruhat–Tits building, and the action of the groups on the building. This will give us insight into parts of S(SL(n, Qp)). We will focus on limits of groups of involutions in SL(2, Qp) (joint with Corina Ciobotaru), and time permitting, discuss limits of other subgroups, based on joint work with Ciobotaru and Alain Valette.