Valuations and Schubert matroids

Valuations are a classical tool in convex geometry; examples include the Euler characteristic, Lebesgue measure, and mixed volume. However, in the past two decades, valuations have also gained prominence in the theory of matroids. As every matroid gives rise to a matroid polytope, one can develop a theory of subdivisions and valuations for matroids. In this talk, we’ll introduce valuations on matroids and examine a result of Derksen and Fink which says that Schubert matroids are a basis for matroids modulo valuation.

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Date published: Wednesday, March 26, 2025