Tropical hyperplane arrangements and oriented matroids

I will define the notion of a tropical oriented matroid (TOM), an object which captures the combinatorial structure of a tropical hyperplane arrangement, and shares several of the properties of ordinary oriented matroids. I will show how a TOM determines a subdivision of a product of two simplices, and provide strong evidence that this correspondence is a bijection. I will conclude with several open problems.

The talk will assume no previous knowledge of tropical geometry or matroid theory. This is joint work with Anna Brown and Mike Develin.