Matroids From Hypersimplex Splits

Studying regular subdivisions of a class of convex polytopes which are called hypersimplices naturally leads to a new class of matroids, which we call split matroids. Very many matroids are of this type; e.g., the paving matroids arise as special cases. It turns out that the structural properties of the split matroids can be exploited to obtain new results in tropical geometry. Joint work with Benjamin Schröter.