In this talk, we show that the tropical projective Grassmannian of planes is homeomorphic to a closed subset of the analytic Grassmannian in Berkovich sense. Our proof is constructive and it relies on the combinatorial description of the tropical Grassmannian (inside the split torus) as a space of phylogenetic trees by Speyer-Sturmfels. We also show that both sets have piecewiselinear structures that are compatible with our homeomorphism and characterize the fibers of the tropicalization map as affinoid domains with a unique Shilov boundary point. Our homeomorphism identify each point in the tropical Grassmannian with the Shilov boundary point on its fiber. Time permitted, we will discuss the combinatorics of the aforementioned space of trees inside tropical projective space. This is joint work with M. Haebich and A. Werner (Math. Ann. (2014), in press).
Tuesday, April 22nd, at 4:00pm in HBH 227Return to talks from Spring 2014