Equiangular Lines and Eigenvalue Multiplicity - ICBS 2024

Explore the fascinating world of equiangular lines in high-dimensional space through this 56-minute lecture by Yufei Zhao at BIMSA. Delve into the longstanding problem of determining the maximum number of equiangular lines separated by a fixed angle in high dimensions. Discover the key solution ingredient: a new theorem in spectral graph theory stating that the adjacency matrix of a connected bounded degree graph has sublinear second eigenvalue multiplicity. Learn about configurations of lines passing through the origin that pairwise make the same angle, and gain insights into further research directions and open problems in this field. Enhance your understanding of advanced mathematical concepts at the intersection of geometry and graph theory.