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Spencer Backman: Simplicial generation of Chow rings of matroids

Time: Wed 2022-02-23 15.15 - 16.15

Location: Zoom meeting ID: 654 5562 3260

Participating: Spencer Backman

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Abstract: In 2015 Adiprasito, Huh, and Katz settled the Heron–Rota–Welsh conjecture that the absolute value of the coefficients of the characteristic polynomial of a matroid are log-concave. Their approach was to show that these coefficients can be interpreted as intersection numbers in the Chow ring of a matroid. They then demonstrated that the Chow ring of a matroid has a working Hodge theory despite not being the Chow ring of a smooth projective variety, and applied the Hodge-Riemann relations to establish the desired log-concavity. I will describe an alternate collection of generators for the Chow ring of a matroid which we call simplicial generators. These generators have a rich combinatorial and geometric nature, and I will emphasize how they provide a natural matroidal extension of Postnikov’s study of generalized permutahedra via standard simplices. As an application, our presentation offers an alternate proof of the AHK log-concavity result. This talk represents joint work with Chris Eur and Connor Simpson.

Zoom meeting ID: 654 5562 3260

Zoom link: