MAAD talk - An introduction to noncrossing partitions

Title: An introduction to noncrossing partitions

Abstract: Given a configuration of points in the plane, its "convex hull" is the smallest convex polygon which contains those points—imagine the area contained by a rubber band which is being held in place by some thumb tacks. Relatedly, a "noncrossing partition" of points in the plane is a way of grouping those points into parts so that the convex hulls of the parts do not overlap. In this talk, I will provide an overview of noncrossing partitions and some results from previous work of mine with undergraduate coauthors Cohen, Harsh, Martin (2022); Fang, Jiang, Lin, Lindenmuth, Pokras, Root (2024); and Root (2025). This will include some connections to combinatorics and abstract algebra, but no prior background will be needed.