Mario Sanchez: Permutahedra, Subdivisions, and Derived Categories

ABSTRACT: The derived category of a variety is an important and difficult invariant. In this talk, I discuss a purely convex-geometric and combinatorial approach to these categories for toric varieties through the study of subdivisions of polytopes. Along the way, we will run into the curious question of studying the contractibility of set differences of polytopes. I will focus on the toric variety of the permutahedron which has played an important role in many recent developments in matroid theory. I discuss how this derived category can be described through matroids.