|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|
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.
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