报告题目：Some improved remainder estimates in Weyl’s law
报 告 人：郭经纬
工作单位：中国科技大学
报告时间：2020-12-11 16:40-18:00；
腾讯会议ID：827 143 702
报告摘要：
This talk is about an application of harmonic analysis to a problem from spectral geometry. One of the most important objects in spectral geometry is the eigenvalue counting function, say, for the Dirichlet Laplacian associated with planar domains. The simplest examples of such domains are squares, disks and ellipses. 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. I will introduce background briefly and explain how to transfer the above problem into problems of counting lattice points, to which tools from analysis and analytic number theory can be applied. I will mention our progresses for disks, annuli and balls in high dimensions, joint with Wolfgang Mueller, Weiwei Wang and Zuoqin Wang.
报告人简介：
郭经纬，男，教授。2011年毕业于威斯康辛大学麦迪逊分校，获博士学位；2011年-2014年在美国伊利诺伊厄巴纳-香槟分校任助理教授。2014年9月入职中国科学技术大学数学学院，任专任研究员。近年来，他主要从事经典调和分析与谱几何相关问题的研究。迄今为止，在美、英、德、日、波兰、西班牙等国有影响的刊物发表高水平论文9篇。
