Date: 2 March 2018 Location: Hempfield High School, Room 213 Speaker: Ron Umble, Millersville University Title: The Coherent Framed Join and Biassociahedra Abstract. We construct the coherent framed join of finite ordered sets, form the reduced coherent framed join as an appropriate quotient, and use the combinatorics of the reduced framed join to construct the biassociahedra $KK_{n,m}$. In the ranges $1\leq m\leq3$ and $1\leq n\leq3$, which are sufficient for our applications, the cellular chain complex $C_*(KK)$ is canonically isomorphic to the free matrad $\mathcal{H}_{\infty}$.