In this series of lectures, we will explore noncrossing partitions within the realm of finite reflection groups.
In the first lecture, I will introduce you to noncrossing partitions as reflection group elements, present how to visualize them as set partitions in the classical types ABCD, and present some counting formulas.
In the second and third lecture, we will discuss the noncrossing Cataland. We will see their incarnations as clusters in cluster algebras and as specific subword complexes, and also the noncrossing partition lattice and the Cambrian lattice. We conclude by also considering noncrossing Fuss-Cataland by extending our discussion from finite reflection
groups to their associated Artin groups.