北航数学论坛学术报告

---分析、偏微分方程与动力系统讨论班(2026春季第15讲)

Geometric measure of nodal, critical and singular sets for solutions of degenerate equations

Yannick Sire（Johns Hopkins University）

时间：2026年08月12日（周三）下午14:50-15:30

地点：北航学院路老主楼 主410

摘要: I will describe recent results on the “size” of various sets associated to solutions of some elliptic PDEs whose coefficients are degenerate or singular. In the case of eigenfunctions of the associated second order operators, these estimates are related to some famous conjectures by Yau (formulated in a more classical setting). Degenerate PDEs appear in a lot of different contexts like conical spaces, realizations of Dirichlet-to-Neumann maps, Poincare-Einstein manifolds in conformal geometry, etc. I will describe several strategies to get these estimates, leading for some of them to sharp bounds. Along the way, I will also describe some eigenfunction and cluster estimates, which are very much related to this topic.

报告人简介: Yannick Sire，著名法国数学家，现任美国约翰霍普金斯大学数学系终身教授、副主任（分管研究生教学），在偏微分方程、调和分析、动力系统等领域做出了一系列杰出的工作。2018年入选西蒙斯基金会数学会士，2021年入选美国数学会会士。

欢迎大家参加！