学术报告三十三:郭经纬—The two-term Weyl formulas for planar disks and annuli

发布时间:2019-11-01

报告时间2019116日(星期三)10:10-11:10

报告地点翡翠湖校区科教楼B1710

报告郭经纬

工作单位中国科学技术大学数学科学学院


报告人简介:

郭经纬,中国科技大学特任研究员,主要从事于基础数学的分析学方向的研究。近年来关注的重点是将分析学的方法应用于数论和谱几何的问题的研究中。尤其在格点问题和Weyl定律的渐近展开问题里获得了一系列目前的最佳结果。

  

报告简介:

  One of the most important objects in spectral geometry is the eigenvalue counting function, say, of the Dirichlet Laplacian associated with planar domains. 

The simplest examples of domains are squares, disks, annuli, etc. It is well-known that for each of these domains its eigenvalue counting function has an asymptotics containing two main terms and a remainder of size $o(\mu)$. (Such an asymptotics is usually called Weyl's law.) To improve the estimate of the remainder term had been one of the most attractive problems in spectral geometry for decades.

In this talk I will first introduce background and the work by Y. Colin de Verdiere on the two-term Weyl formula for planar disks. Then I will explain how to improve his result by using tools from analysis and analytic number theory and how to extend it from disks to annuli. This is our recent work joint with Wolfgang Mueller, Weiwei Wang and Zuoqin Wang.