MATH Seminar

Title: Forbidden subgraphs and spherical two distance sets
Seminar: Discrete Math
Speaker: Zilin Jiang of Arizona State University
Contact: Liana Yepremyan, liana.yepremyan@EMORY.EDU
Date: 2022-04-01 at 4:00PM
Venue: MSC W303
Abstract:
Given a real number $\lambda$, what can we say about the family G($\lambda$) of graphs with eigenvalues bounded from below by -$\lambda$The Cauchy interlacing theorem implies that that the family G($\lambda$) is closed under taking (induced) subgraphs. Similar to Wagner’s theorem, which describes the family of planar graphs by finite forbidden minors, it is natural to ask for which $\lambda$ the family G($\lambda$) has a finite forbidden subgraph characterization. In this talk, I will illustrate the key ideas in answering this question, and I will demonstrate a peculiar connection to spherical two distance sets — a set of unit vectors in a Euclidean space the pairwise inner products of which assume only two values. Joint work with Alexandr Polyanskii, Jonathan Tidor, Yuan Yao, Shengtong Zhang and Yufei Zhao.