報告題目：Bounds of nodal sets of eigenfunctions

報告人：朱久義（Louisiana State University）

報告時間：2021年12月15日上午11:00-12:30

騰訊會議ID：510 463 682

報告人簡介：朱久義, 路易斯安那州立大學助理教授。2008年碩士畢業(yè)于湖南師范大學, 2013年博士畢業(yè)于韋恩州立大學。2013-2016年在約翰霍普金斯大學擔任J.J. Sylvester Assistant Professor. 主要研究方向是偏微分方程。兩次獲得美國自然科學基金資助，獨立PI. 在AJM, ARMA, Analysis & PDE, CPDE等雜志上發(fā)表多篇論文。

報告摘要：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.

邀請人：謝君輝

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