Combinatorics Seminar

In his 2005 PhD thesis on tropical linear spaces, Speyer conjectured an upper bound on the number of interior faces in a matroid base polytope subdivision of a hypersimplex. This conjecture can be reduced to determining the sign of the Euler characteristic of a certain K-class associated with a matroid. In recent joint work with Alex Fink, we prove this conjecture by showing that the requisite Euler characteristic is non-positive for all matroids. In this talk, I will provide an overview of our strategy and zoom in on the step that extends results from realizable matroids to all matroids.