报告题目：Harmonic mappings with free boundaries and their heat flows

报告摘要：The aim of this series of lectures is to describe recent advances in the theory of harmonic mappings with free boundaries.Those maps are instrumental in several geometric problems such as extremal metrics for the Steklov spectrum.I will describe both the elliptic and the parabolic theory, emphasizing in existence and regularity aspects. I will also mention several open problems along the way.A tentative plan of the lectures would be:

1-Theory of Standard Harmonic mappings: existence, regularity and their parabolic deformation.

2-Harmonic maps with free boundary: partial regularity.

3-Approach to harmonic maps with free boundary via the Dirichlet-to-Neumann map; half-harmonic maps of Da Lio and Riviereand construction of their heat flows.

4-Partial regularity of heat flowsandPlateau flow of Struwe.

报告人简介：Yannick Sire，法国人，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。

报告时间：2025年7月28日、29日8：45-12:00

报告地点：同析4号楼506教室