Chabauty limits of fixed point groups of p-adic involutions

Let G be a connected reductive group defined over a non-Archimedean local field k. Endow G with a k-involution and take H to be the fixed-point subgroup in G of that involution. In this talk I will report on some of my recent results regarding Chabauty limits of H(k) inside G(k). Although the results are similar to the real and complex cases, the techniques are totally different and with a strong geometric flavor. Some of the main actors are the Bruhat—Tits building associated with G(k) and basic methods from CAT(0) geometry.