Name:  Yufei Zhao  (MIT)

Title:  Equiangular lines and eigenvalue multiplicity

Abstract:

I will discuss our solution to a longstanding discrete geometry problem where we determined the maximum number of lines in high dimension pairwise separated by a fixed angle.  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.