Title: 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, along with extensions and open problems (e.g., 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
Here is the zoom link is: https://wse.zoom.us/j/95448608570