Abstract: 

This talk aims to advertise a pattern/phenomenon that has emerged in many different mathematical areas during the past decades but is not currently well-understood via an example: Bott--Samelson rings for Coxeter groups. This is the product of a project of the PACE program at Peking University last year, joint with Lin Sun (Fudan University), Shihao Wang (Tsinghua University) and Haoyu Zhu (Sun Yat-sen University).