SFU NTAG Seminar: Andrew Berget

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 matroid class in the K-theory of the permutohedral variety. In a recent joint work with Alex Fink, we prove Speyer's conjecture by showing that the requisite Euler characteristic is non-positive for all matroids, and extend this to a statement about pairs of matroids on the same ground set. In this talk, I will provide an overview of our strategy and zoom in on how we extend geometric results for realizable pairs of matroids to all pairs.