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Algebra Seminar

Date:
-
Location:
CB 336
Speaker(s) / Presenter(s):
Austin Alderete

Title: Tropical Matroid Homology

 

Abstract: The intersection ring of matroids arises from the restriction of tropical intersection theory to Bergman fans. As an algebraic object, the intersection ring encodes many matroid invariants as homomorphisms and is naturally bigraded by the rank and ground set of the matroids which generate it. The matroid operations of deletion and contraction give rise to boundary maps, producing a tropical analog of the Kontsevich homology. We give an affirmative answer to the conjecture that these homology groups are trivial on the full intersection ring and show that these groups be used to measure whether a class of matroids is closed under certain extensions. We further extend this notion of homology to Chow rings of arbitrary matroids.

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