Speaker: Michael Dougherty

Title: Catalan Numbers and the Braid Group

 

In combinatorics, the integer sequence known as the Catalan numbers lies at the center of several different counting problems. Aside from being the solution to many enumerative questions, these numbers also arise in seemingly disparate topics such as Temperley-Lieb algebras, hyperplane arrangements, and algorithmic questions for Coxeter and Artin groups. In this talk, we will discuss the basics of Catalan numbers and an appearance of their structure in the braid group.