Fully Commutative Elements in Complex Reflection Groups

Abstract: Originally studied in Coxeter groups, fully commutative elements are those whose reduced expressions can be transformed into one another using only commutations. This talk will begin with concrete examples in the symmetric group, and extend to complex reflection groups. We'll show how these elements are tied to pattern avoidance in permutations and the natural bases of the Temperley-Lieb algebra. We'll highlight recent developments and share some open questions. This talk will assume no previous knowledge of these topics, and will be accessible to anyone who is interested.