Log-concavity of Polynomials Arising from Equivariant Cohomology

Attend this special year seminar talk where Yairon Cid-Ruiz from North Carolina State University explores the log-concavity of polynomials arising from equivariant cohomology. Discover how volume polynomials of projective varieties relate to Lorentzian polynomials, as established by Brändén and Huh, and learn about the dual notion of covolume polynomials introduced by Aluffi through cohomology classes of subvarieties in projective space products. The lecture focuses on equivariant cohomology classes of torus-equivariant subvarieties in matrix spaces, demonstrating how these class-representing polynomials (with appropriate sign changes) function as covolume polynomials for a wide range of torus actions. If time allows, explore a description of cohomology rings of smooth complex varieties using generic Macaulay inverse systems over integers. This one-hour talk, based on joint work with Yupeng Li and Jacob Matherne, takes place at 2:00pm in Simonyi 101 on March 12, 2025, as part of the Institute for Advanced Study's Special Year Seminar series.