Introduction and overview of the Kahler package

I will recap the framework developed by June Huh and collaborators for establishing Rota’s Conjecture on the log-concavity of characteristic polynomials of matroids. In particular, I will discuss how the existence of Hodge-Riemann relations in the Chow ring of a matroid imply log-concavity of the characteristic polynomials. Furthermore, I will outline how we can use properties of “volume polynomials” of the Chow ring to establish the existence of the desired Hodge-Riemann relations. At the conclusion of this talk, we will discuss the plan for the talks for the rest of the semester.

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Date published: Wednesday, January 29, 2025