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Derived Categories of the Permutahedral Varieties

Derived Categories of the Permutahedral Varieties

The derived category of a variety is an important invariant that is difficult to compute. One way to describe this category is to hope that it contains a nice set of sheaves known as a full strongly exceptional collection. I discuss a convex-geometric and combinatorial approach to finding tilting sheaves for toric varieties through the study of polytopal subdivisions and the homology of set difference of polytopes. I will focus on the toric variety of the permutahedron, also known as the Losev-Manin space, which has played an important role in many recent developments in matroid theory. Much of this work can be seen as a categorification of the ongoing story in algebraic combinatorics of the McMullen polytope algebra and the theory of valuations.

Refreshments at 3:45PM.

## Department of Mathematics and Statistics