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姜子麟 博士:Forbidden subgraphs and spherical two-distance sets

本站小编 Free考研考试/2021-12-26


Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars
Speaker: 姜子麟 博士，Arizona State University
Inviter:
Title:
 Forbidden subgraphs and spherical two-distance sets
Time & Venue:
 2021.07.27 10:00-11:30 腾讯会议：225 342 754
Abstract:
 A set of unit vectors in a Euclidean space is called a spherical two-distance set if the pairwise inner products of these vectors assume only two values α>β. It is known that the maximum size of a spherical two-distance grows quadratically as the dimension of the Euclidean space grows. However when the values α and β are held fixed, a very intricate behavior of the maximum size emerges. Building on our recent resolution in the equiangular case, that is α+β=0, we make a plausible conjecture which connects this behavior with spectral theory of signed graphs in the regime β<0<α, and we confirm this conjecture when α+2β<0 or (1?α)/(β?α) < 2.0198. Joint work with Alexandr Polyanskii, Jonathan Tidor, Yuan Yao, Shengtong Zhang and Yufei Zhao.

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