Title: Equiangular lines and second eigenvalue multiplicity

Abstract (plaintext):

A family of lines passing through the origin in an inner product space is said to be equiangular if every pair of lines defines the same angle. In 1973, Lemmens and Seidel raised what has since become a central question in the study of equiangular lines in Euclidean spaces. 

They asked for the maximum number of equiangular lines in R^r with a common angle of arccos(1/(2k-1)) for any 

integer k> 1. We show that the answer equals r-1+floor((r-1)/(k-1)), provided that r is at least exponential in a polynomial in k. This improves upon a recent breakthrough of Jiang, Tidor, Yao, Zhang, and Zhao, who showed that this holds for r at least doubly exponential in a polynomial in k.

Joint work with Igor Balla.