School Colloquium——Hot Spots Conjecture
报告人：桂长峰 (澳门大学)
时间：2025-12-26 14:00-15:00
地点：智华楼四元厅
报告摘要：In the study of the classic heat equation, it is observed that the hottest spot tends to move to the boundary when completely insulated. The hot spots conjecture, proposed by Rauch in 1974, asserts that the second Neumann eigenfunction of the Laplacian achieves its global maximum (the hottest point) exclusively on the boundary of the domain. Notably, for triangular domains, the absence of interior critical points was recently established by Judge and Mondal in [Ann. Math., 2022]. Nevertheless, several important questions about the second Neumann eigenfunction in triangles remain open. In this talk, I shall present a complete resolution of these issues.
Our approach employs fundamental ideas such as continuity via domain deformation, and comparison of eigenvalues of various eigenvalue problems and the maximum principle.
This is a joint work with Hongbin Chen and Ruofei Yao.
报告人简介：桂长峰，澳门大学科技伊人直播
讲座教授、数学系主任，澳大发展基金会数学杰出学人教授，曾任加拿大英属哥伦比亚大学助理教授， 副教授，美国康涅狄格大学教授，美国德州大学圣安东尼奥分校丹．帕尔曼应用数学冠名讲座教授。研究方向为非线性偏微分方程、图像分析和处理，在国际顶级期刊如《Annals of Mathematics》《Inventiones Mathematicae》《Communications on Pure and Applied Mathematics》发表多篇论文。曾获颁加拿大太平洋数学研究所研究成果奖、加拿大数学中心Aisensdadt 奖、IEEE信号处理协会最佳论文奖、中国国家自然科学基金海外合作基金（海外杰青）等奖项。入选国家级高层次人才计划。是美国数学学会首届会士、美国西蒙斯会士、美国科学促进会（AAAS）会士。
