Mario Sanchez: Noncrossing partitions

Mario Sanchez: Noncrossing partitions.

Abstract

Noncrossing partitions are a subset of partitions that behave nicely with respect to an underlying total order of the ground set. These simple to define objects appear in topics ranging from total positivity to noncommutative probability. In this talk, we will focus on the combinatorial aspects of noncrossing partitions and their relation with a few other topics in combinatorics. In the process of building noncrossing partitions of other types, we will be forced to think about Coxeter groups in a different way.