Algebraic Graph Theory Seminar - Ingemar Bengtsson

Title: Equiangular lines and algebraic number theory

Abstract: It is believed that SICs, that is maximal equiangular tight frames, exist in all complex vector spaces. To construct them we use the Weyl-Heisenberg groups, and hence the cyclotomic numbers (roots of unity). But we need more. I will present an infinite sequence of dimensions in which we can propose an explicit "formula" for a SIC. It relies on a conjecture by Stark, who proposed an analogue of the roots of unity for much more interesting number fields. It also relies on a result in a University of Waterloo PhD thesis.