数学学院学术报告

--- 分析、偏微分方程与动力系统讨论班(2024秋季第9讲)

Counting lattice points and eigenvalues

郭经纬 

（中国科学技术大学）

时间：2024年11月20日 （周三上午） 10:00-11:00am

地点：#腾讯会议：482-344-9963 会议密码：123456

摘要：In this talk, I will first introduce a classic problem from number theory of counting lattice points in certain Euclidean domains (for example, planar disks and convex domains with smooth boundary and nonvanishing Gaussian curvature). I will explain how to apply the oscillatory integral theory to this kind of problem.

I will next introduce another classic problem from spectral geometry of counting eigenvalues for Dirichlet Laplacian (aka the Weyl's law) on special domains with boundary (like squares, disks, annuli and high-dimensional versions). I will explain how to connect this kind of problem to that of counting lattice points, and mention our results on some improved estimates of the remainder of the Weyl’s law.

报告人简介：郭经纬, 中国科学技术大学副教授，研究方向为调和分析，已在高水平数学期刊Math. Ann.等发表论文十余篇。

欢迎大家参加！