3:00–4:00 pm
Eckhart Hall 5734 S University Room 202 Chicago, IL 60637
Equiangular lines and eigenvalue multiplicities
Abstract:
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.
My talk will discuss these problems and their connections. Here is an open problem that I would like to understand better: what is the maximum possible second eigenvalue multiplicity of a connected bounded degree graph?
Joint work with Zilin Jiang, Jonathan Tidor, Yuan Yao, and Shengtong Zhang