Codes and Expansions (CodEx) Seminar

Gene S. Kopp (Purdue University)
A step toward a constructive proof of Zauner's conjecture

In 1999, Zauner conjectured that a maximal set of \(d^2\) equiangular lines always exists in \(\mathbb{C}^d\). Such sets are called SICs and are only known to exist for finitely many \(d\). The algebraic equations defining SICs also give rise to related objects known as ghost SICs. Using ideas from number theory, we give a conjectural formula for SICs in every dimension as Galois conjugates of ghost SICs, which we in turn construct from special values of analytic functions. We thus show that Zauner's conjecture would follow from a special function identity together with Tate's refinement of a conjecture of Stark.