Title: The cohomology of abelian Hessenberg varieties
Speaker: Martha Precup (Northwestern)
Abstract: Hessenberg varieties are subvarieties of the flag variety with important connections to representation theory, algebraic geometry, and combinatorics. These varieties have gained recent attention due to a conjecture of Shareshian and Wachs relating the chromatic quasisymmetric function of the incomparability graph of a unit interval order to the dot action representation on the cohomology of an associated regular semisimple Hessenberg variety. In this talk, I will report on recent joint work with M. Harada in which we prove an inductive formula for the Betti numbers of certain regular Hessenberg varieties called abelian Hessenberg varieties. Using a theorem of Brosnan and Chow, this formula yields an inductive description of the dot action representation.
Seminar URL: https://research.math.osu.edu/gcis/
