报告人： 姚若飞 教授

报告题目： Recent Progress on the Hot Spots Conjecture and Related Topics

时间： 2026年7月7日（周二）16:00—16:40

地点： 线上腾讯会议（会议号：750 913 971）

报告摘要：
The Hot Spots Conjecture is a classical problem in partial differential equations and spectral geometry, originating from a question posed by Rauch in 1974. It asserts that the global extrema of the second Neumann eigenfunction of the Laplacian are attained exclusively on the boundary of a domain. In this talk, we will present several recent developments related to the conjecture, including qualitative properties of the second Neumann eigenfunction on triangles and certain symmetric domains, eigenvalue inequalities, and the characterization of multiple eigenvalues on symmetric quadrilateral domains. This talk is based on a series of joint works with Hongbin Chen, Haiyun Deng, Changfeng Gui, Xuyong Jiang, Xuefeng Wang, Ke Wu, Xiaoping Yang, and Jun Zou.

报告人简介：
姚若飞，西安交通大学博士，曾在中南大学从事博士后研究。2020年12月入职华南理工大学，现任教授。主要研究方向为偏微分方程理论，尤其关注热点猜想以及椭圆型偏微分方程解的对称性与单调性问题。相关研究成果发表于 Inventiones Mathematicae、Mathematische Annalen、Journal of Functional Analysis、SIAM Journal on Mathematical Analysis、Calculus of Variations and Partial Differential Equations、Nonlinearity、Journal of Differential Equations 等国际期刊。