Gene Kopp

Complex equiangular lines and the Stark conjectures

How many lines can you place through the origin in d-dimensional complex space such that all the pairwise angles between these lines are the same? This is an open question of interest in quantum information theory and frame theory, whose answer is predicted by Zauner's conjecture. As a byproduct of extensive numerical computations, we have a lot of empirical data about the algebraic and Galois-theoretic structure of maximal configurations of complex equiangular lines. Indeed, there is strong evidence of a connection to class field theory and the Stark conjectures (on the leading Taylor coefficient of Hecke L-functions at s=0). We will discuss the history of the conjectures of Zauner and Stark, and we will give a conditional result relating the two conjectures.