【学术报告】Gap distribution of directions of certain planar point sets

报告人：于树澄（中国科学技术大学）

时 间：2024年12月7日14:00

地 点：厦门大学海韵园实验楼S102

内容摘要:

Given a planar point set with a constant density, one can study the limiting distribution of gaps for directions (i.e. projection to the unit sphere) of points from this point set in larger and larger disks. For primitive integer points an explicit formula for the limiting gap distribution function was obtained by Boca, Cobeli, and Zaharescu using analytic number theory. This formula was later extended by Marklof and Strömbergsson for any lattices using homogeneous dynamics. More recently, they showed the limiting gap distribution function exists for point sets of cut-and-project type. The main theme of the dynamical approach is that the limiting gap distribution function is expressed in terms of the measure of certain sets in the corresponding homogeneous space. In this talk I will describe a tail asymptotic formula for the limiting gap distribution functions from this point of view. This is joint work with Gustav Hammarhjelm and Andreas Strömbergsson.

个人简介：

于树澄，中国科学技术大学特任教授，博士生导师。2018年于美国波士顿学院取得数学博士学位，随后在以色列理工、瑞典乌普萨拉大学任职博士后。主要从事齐性动力系统与丢番图逼近等相关领域的研究工作，在PLMS, Math. Ann., Adv. Math.等杂志发表论文十余篇。

联系人：吴伟胜