Problem of the Week
Hilton Memorial Lecture
Matroids are a combinatorial generalization of both graphs and finite point configurations in vector spaces. The latter are called representable matroids. Matroids which are equipped with an additional valuation are called valuated matroids or tropical linear spaces. They are an object of central interest in tropical geometry. I will introduce these matroids and their moduli spaces, the Dressians and tropical Grassmannians, in terms of polyhedral geometry. Moreover, I present recent results which include representability, a new class of matroids called split matroids, and results about facets of secondary polytopes.