The story of noncrossing partitions starts with a Coxeter group W anda Coxeter element c. (If you’re not familiar with Coxeter things, think: W is the symmetric group S_n and c is an n-cycle.) The noncrossing partitions in W are the elements of the interval [1,c]_T in a certain partial order on W (the absolute order). When W is a finite Coxeter group, [1,c]_T is a lattice. In the classical finite types, there are planar diagrams for noncrossing partitions. When W is infinite, [1,c]_T may not be a lattice. In the affine case, McCammond and Sulway embedded W into a larger group in which an analogous interval [1,c] is a lattice (thus proving some longstanding conjectures for Euclidean Artin groups). Their key idea was to factorthe translations in [1,c]_T. I’ll discuss work (including work from Laura Brestensky’s thesis) to construct planar diagrams for noncrossing partitions of classical affine types. The planar diagrams “know” how to factor translations, and thus yield new insights into the McCammond-Sulway construction. I’ll discuss all of this (assuming no prior knowledge of Coxeter groups, Artin groups, or noncrossing partitions) and may mention some generalizations where the topology of the diagrams gets more interesting. Much of this is joint work with Laura Brestensky.

Jointly in person and virtually on Zoom. SAS 2225 for in-person participation. The Zoom link is sent out to the Algebra and Combinatorics mailing list, please contact Corey Jones at cmjones6@ncsu.edu to be added.