Giovanni Paolini (Università di Bologna)

Abstract: In this seminar, we will explore the fascinating world of Coxeter groups and their associated combinatorics, with a particular focus on the weak Bruhat order and the poset of noncrossing partitions. These combinatorial structures provide powerful tools for studying algebraic and topological properties of Artin groups arising from finite Coxeter groups, which will be our primary focus in the first half. In the second half, I will describe ongoing efforts aimed at understanding Artin groups arising from infinite Coxeter groups, which are more challenging and mysterious.