# Equiangular lines with a fixed angle

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Yufei Zhao, MIT
Fine Hall 224

Solving a longstanding problem on equiangular lines, we determine, for each given fixed angle and in all sufficiently large dimensions, the maximum number of lines pairwise separated by the given angle. A key ingredient is a new result in spectral graph theory: the adjacency matrix of a connected bounded degree graph has sublinear second eigenvalue multiplicity.

Joint work with: Zilin Jiang, Jonathan Tidor, Yuan Yao, and Shengtong Zhang