Seminar| Institute of Mathematical Sciences
Time: Wednesday, November 6th, 2024 , 14:00-15:00
Location: IMS, RS408
Speaker: Tao Gui, Beijing International Center for Mathematical Research
Abstract: We study the cohomology ring of the Bott--Samelson variety. We compute an explicit presentation of this ring via Soergel's result, which implies that it is a combinatorial invariant. We prove that it is a Koszul algebra and we provide a quadratic (reduced) Gröbner basis. Furthermore, we prove that it satisfies the whole Kähler package, including the Poincaré duality, the hard Lefschetz theorem, and the Hodge--Riemann bilinear relations. This is the product of a project of the PACE program (a research experience for undergraduates) at Peking University, joint with Lin Sun (Fudan University), Shihao Wang (Qsinghua University) and Haoyu Zhu (Sun Yat-sen University).