Log-concavity of Polynomials Arising from Equivariant Cohomology

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. If time permits, we shall present a description of the cohomology rings of smooth complex varieties in terms of a generic Macaulay inverse system over the integers.

This is based on joint work with Yupeng Li and Jacob Matherne.