Forbidden subgraphs and spherical two-distance sets

主 讲 人 ：姜子麟    

活动时间：07月21日13时00分    

地      点 ：Zoom 会议，https://us06web.zoom.us/j/88247009286?pwd=UlhXSmlZdG1nSUpZWmI0VkM0YUVYQT09 （会议号：882 4700 9286 密码：462643）

讲座内容：

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 and β. It is known that the maximum size of a spherical two-distance grows quadraticallyas the dimension of the Euclidean space grows. However when the values α and βare held fixed, a very intricate behavior of the maximum size emerges. Buildingon our recent resolution in the equiangular case, that is β = -α, we make aplausible conjecture which connects this behavior with spectral theory ofsigned 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.

主讲人介绍：

姜子麟于 2011 年在北京大学取得数学学士学位，并于 2016 年在卡内基梅隆大学取得算法、组合与优化的博士学位。此后，他于 2016 年至 2018 年间在以色列理工大学担任博士后研究员，并于 2018 年至 2020 年底在麻省理工学院继续担任应用数学教员（博士后职位）。他目前在亚利桑那州立大学担任助理教授。姜子麟的研究兴趣包括离散几何、极值图论和拓扑组合。

发布时间：2023-07-15 10:04:43