[학술] [세미나] 2024 아주 위상조합 세미나 안내(6/18 화)
- 수학과 BK21
- 관리자
- 작성일 2024-06-17
- 조회수 13
일시 | 2024.06.18.(수) 16:30 ~ 17:30 |
장소 | 온라인(ZOOM) |
발표자 | Mikiya Masuda (Osaka Central Advanced Mathematical Institute) |
Title | REGULAR SEMISIMPLE HESSENBERG VARIETIES OF DOUBLE LOLLIPOP TYPE |
Abstract | The solution of Shareshian-Wachs conjecture by Brosnan-Chow (and Guay- Paquet unpublished) linked together graded chromatic symmetric functions on unit interval graphs (combinatorics) and the cohomology of regular semisimple Hessen- berg varieties (geometry). Regular semisimple Hessenberg varieties are subvarieties of the full flag variety Fl(n) parametrized by Hessenberg functions h: [n] → [n] (equivalently Dyck paths). The family of connected regular semisimple Hessenberg varieties X(h) contains Fl(n) itself (as the largest h) and the permutohedral variety Permn (as the smallest h). The cohomology rings of both Fl(n) and Permn are generated in degree two as is well-known but the cohomology ring of X(h) is not necessarily generated in degree two. It turns out that it is generated in degree two if and only if h is of double lollipop type. I will explain the idea of the proof. This is joint work with Takashi Sato. |