Commutative Algebra and Algebraic Geometry: The Fellowship of the Ring: Chow rings of matroids, ring of matroid quotients, and beyond

Seminar | February 26 | 5-6 p.m. | 939 Evans Hall

 Chris Eur, UC Berkeley

 Department of Mathematics

We introduce a certain nef generating set for the Chow ring of the wonderful compactification of a hyperplane arrangement complement. This presentation yields a monomial basis of the Chow ring that admits a geometric and combinatorial interpretation with several applications. Geometrically, one can recover Poincare duality, compute the volume polynomial and verify its log-concavity, and identify a portion of a polyhedral boundary of the nef cone. Combinatorially, one can generalize Postnikov's result on volumes of generalized permutohedra, prove Mason's conjecture on the log-concavity of independent sets for certain matroids, and define a new valuative invariant of a matroid that measures its closeness to uniform matroids. This is an on-going joint work with Connor Simpson and Spencer Backman.