报告题目：Bounds of nodal sets of eigenfunctions

报告人：朱久义（Louisiana State University）

报告时间：2021年12月15日上午11:00-12:30

腾讯会议ID：510 463 682

报告人简介：朱久义, 路易斯安那州立大学助理教授。2008年硕士毕业于湖南师范大学, 2013年博士毕业于韦恩州立大学。2013-2016年在约翰霍普金斯大学担任J.J. Sylvester Assistant Professor. 主要研究方向是偏微分方程。两次获得美国自然科学基金资助，独立PI. 在AJM, ARMA, Analysis & PDE, CPDE等杂志上发表多篇论文。

报告摘要：Motivated by Yau's conjecture, the study of the measure of nodal sets (Zero level sets) for eigenfunctions has been attracting much attention. We investigate the measure of nodal sets for Steklov, Dirichlet and Neumann eigenfunctions in the domain and on the boundary of the domain. For Dirichlet or Neumann eigenfunctions  in the analytic domains, we show some sharp upper bounds of  nodal sets  which touch the boundary. We will also discuss some upper bounds of nodal sets for  eigenfunctions of general eigenvalue problems arising from Chladni patterns, which were discovered more than 200 years ago. Furthermore, some recent study of nodal sets in periodic elliptic homogenization will be discussed. Part of the talk is based on joint work with Carlos Kenig, Fanghua Lin and Jinping Zhuge.

邀请人：谢君辉

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