Algebraic Graph Theory Seminar - Ingemar Bengtsson

Monday, October 31, 2022 11:30 pm - 11:30 pm EDT (GMT -04:00)

Title: Equiangular lines and algebraic number theory

Speaker: Ingemar Bengtsson
Affiliation: Stockholm University
Location: contact Sabrina Lato for Zoom link

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.