Log-concavity of Polynomials Arising from Equivariant Cohomology, Yupeng Li (Duke/Michigan State) -- Thursday, June 5th, 2025

A remarkable result of Brändén and Huh tells us that volume polynomials of projective varieties are Lorentzian polynomials. The dual notion of covolume polynomials was introduced by Aluffi by considering the cohomology classes of subvarieties of a product of projective spaces. In this talk, we shall address the equivariant cohomology classes of torus-equivariant subvarieties of the space of matrices. For a large class of torus actions, we shall show that the polynomials representing these classes (up to suitably changing signs) are covolume polynomials in the sense of Aluffi. As an application, we shall show that several polynomials in Schubert calculus and in matroid theory have saturated Newton polytopes and have discretely log-concave coefficients. This is based on joint work with Yairon Cid-Ruiz and Jacob Matherne.

Organizers: Ian Cavey, Andrew Hardt, Alexander Yong