报告人：桂长峰

报告时间：2025年12月10日（周三）上午9：00---

报告地点：腾讯会议:369-453-832

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：桂长峰是澳门大学数学系讲座教授、数学系主任，澳大发展基金会数学杰出学者。1991年在美国明尼苏达大学获得博士学位，曾入选国家级人才计划和海外高层次人才，并于2013年当选美国数学会首届会士，同时也是美国科学促进会会士。曾获IEEE最佳论文奖、加拿大太平洋数学研究所研究成果奖、加拿大数学中心Andrew Aisensdadt奖等荣誉。他主要从事非线性偏微分方程、图像分析和处理的研究，在Allen-Cahn方程的研究、Moser-Trudinger不等式最佳常数的猜想、De Giorgi猜想和Gibbons猜想等方面取得了一系列在国际上有重大影响的工作，在《Annals of Mathematics》、《Inventiones Mathematicae》、《Communications on Pure and Applied Mathematics》等国际顶尖期刊发表论文90余篇。