Ethan Dlugie (Brown University)
Title: Truncated Braid Groups and Platonic Solids
Abstract: In the 1950s, Coxeter considered the quotients of braid groups given by adding the relation that all half Dehn twist generators have some fixed, finite order. He found a remarkable formula for the order of these groups in terms of some related Platonic solids. Despite the inspiring apparent connection between these topological and geometric objects, Coxeter’s proof boils down to a finite case check that doesn't shed much light on the structure present. I’ll explain recent work that gives an interpretation of the truncated 3-strand braid group that makes the connection with Platonic solids clear, using down-to-earth geometric and algebraic topological tools.
We will gather in the lounge for teatime after the talk, and then we will go for dinner with Ethan.