Coxeter groups are groups that appear throughout algebra and geometry, usually in the form of groups generated by reflections. In this mini-course, we will introduce Coxeter groups, focusing on the most important example: the symmetric group. Our main goal is to understand two important partial orderings on the elements of Coxeter groups: the Bruhat order and the weak order. Bruhat order is closely tied to Schubert calculus and flag varieties, and weak order has applications to root systems and cluster algebras. We will become comfortable thinking about these orders from different perspectives, and discuss some of their applications in algebra and geometry.
Workshop: CMND 2026 Thematic Program
Schedule: Undergraduate Mini-Course Schedule