AGT: Equiangular lines and algebraic number theory

Talk by Ingemar Bengtsson.

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.