中科院数学与系统科学研究院

数学研究所

中科院华罗庚数学重点实验室

华罗庚青年数学论坛

学术报告

报告人：姜子麟 博士（Arizona State University）

题  目：Eigenvalue multiplicity and equiangular lines

时  间：2021.07.26（星期一），10:00-11:30

地  点：腾讯会议：319 120 741

摘  要：A set of lines through the origin in a Euclidean space is called equiangular if they are pairwise separated by the same angle. It is known that the maximum size of an equiangular set of lines grows quadratically as the dimension of the Euclidean space grows. However, when the angle is held fixed, a very different yet intricate behavior of the maximum size emerges. In this talk, I will explain how the determination of this behavior connects to some central notions in spectral graph theory, namely, the maximum eigenvalue of a graph and the multiplicity of the second largest eigenvalue. Joint work with Alexandr Polyanskii, Jonathan Tidor, Yuan Yao, Shengtong Zhang and Yufei Zhao.
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  报告人： 姜子麟 博士（Arizona State University）

题  目：Forbidden subgraphs and spherical two-distance sets

时  间：2021.07.27（星期二），10:00-11:30

地  点：腾讯会议：225 342 754

摘  要：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.