Birational geometry of generalized Hessenberg varieties and the Shareshian-Wachs conjecture (Young-Hoon KIEM, Korea Institute for Advanced Study)

01.04.2025 15:15 – 16:30

Regular semisimple Hessenberg varieties have interesting birational morphisms among them which we can exploit to compute the Tymoczko representations on their cohomology. As a consequence, we obtain elementary proofs of the modular law and the Shareshian-Wach conjecture which relates the Frobenius characteristics with the chromatic quasi-symmetric functions of associated graphs. A similar story can be told for the twin manifolds of Hessenberg varieties where the Frobenius characteristics give us certain LLT polynomials. In this talk, I will discuss these birational geometric aspects of Hessenberg varieties and some applications.

Based on a joint work with Donggun Lee.

Lieu

Bâtiment: Conseil Général 7-9

Room 1-07, Séminaire "Groupes de Lie et espaces de modules"

entrée libre