Speaker: Tao Gui, professor, postdoctoral fellow, Beijing International Center for Mathematical Research(BICMR)

Date: May 16, 2024

Time: 9:30-10:30

Location: E119, Huagangyuan Building, Qingdao Campus

Sponsor: Frontiers Science Center for Nonlinear Expectations, Shandong University; Research Centre for Mathematics and Interdisciplinary Sciences Centre, Shandong University; Sino-Russian Mathematics Center in Qingdao

Abstract:

Hessenberg varieties are subvarieties of the full flag varieties which are defined by a Dyck path (corresponds to a “Hessenberg function”) and a linear transformation. Tymoczko constructed the so called “dot action” of symmetric groups on the cohomology of Hessenberg varieties using the GKM theory, whose Frobenius images are proven to be exactly (the dual) of the corresponding Shareshian--Wachs’s chromatic quasi-symmetric functions by Brosnan--Chow and Guay-Paquet independently. The Stanley--Stembridge conjecture and the stronger (i. e., q-version) Shareshian--Wachs conjecture are reduced to finding a good basis of the cohomology. We will explain the basic language necessary to understand these intricate geometry pictures.

For more information, please visit:

https://www.view.sdu.edu.cn/info/1020/191158.htm