Lethbridge Number Theory and Combinatorics Seminar: Darcy Best

A set of unit vectors $V \subset \mathbb{C}^n$ is called {\it biangular} if for any $u,v \in V, u \neq v$, $$|\langle u,v\rangle| \in \left\{0,\alpha\right\}$$ for some $0 < \alpha < 1$. There are well-known upper bounds on the size of these sets of vectors. We will discuss these upper bounds, and the implications when they are met, including the generation of combinatorial objects such as strongly regular graphs and association schemes.