Where the tame tori are

For any field k and any reductive group G defined over k, the rational classes of maximal k-tori in G can be classified via Galois cohomology. While often useful, this classification doesn’t provide much information about what the maximal k-tori look like. In the 1950s Borel, Harish-Chandra, Kostant, and Sugiura gave a concrete description of what the rational maximal tori look like for real Lie groups.  In this talk we will present a way to classify, via Bruhat-Tits theory, the rational conjugacy classes of maximal tame rational tori in a p-adic Lie group.