Learning seminar in algebraic combinatorics: Tropical linear spaces and buildings

In a previous lecture, we learnt about tropical linear spaces in terms of valuated matroids, or tropical Plucker vectors. In this talk, I'll give a quick overview of some other ways to think about tropical linear spaces: matroid decompositions of the hypersimplex, Chow quotients of the Grassmannian, and membranes. I'll focus on the last of these. A result of Keel and Tevelev states that tropical linear spaces can be identified with membranes, certain subcomplexes of a (Bruhat-Tits) affine building.