Zoom link: https://harvard.zoom.us/j/779283357?pwd=MitXVm1pYUlJVzZqT3lwV2pCT1ZUQT09
Passcode: 657361
Speaker: Yufei Zhao
Title: Equiangular Lines and Eigenvalue Multiplicity
Abstract: Equiangular lines are configurations of lines in n-dimensional space, all passing through the origin, that pairwise make the same angle. Fix an angle, in high dimensions, what is the maximum number of equiangular lines pairwise separated by the given angle? I will discuss the solution to this problem. A key step is in showing that a connected bounded degree graph has sublinear second eigenvalue multiplicity.
These results prompted further investigations into spherical codes and spectral graph theory. I will highlight some ongoing work and open problems