一、报告题目

Morse Index Stability of Biharmonic Maps in Critical Dimension

二、主讲人

Alexis Michelat (瑞士洛桑联邦理工学院)

三、报告时间

2024年1月19日16：00 – 17:30

四、报告地点

Zoom会议号：929 633 31792

五、摘要

The Morse index of a critical point of a Lagrangian is the dimension of the maximal vector space on which the second derivative is negative-definite. In the classical theory, one shows that the Morse index is lower semi-continuous, while the sum of the Morse index and nullity is upper semi-continuous.

Last year, Da Lio, Gianocca, and Riviere developed a new method to show upper semi-continuity results in geometric analysis—that they applied to conformally invariant Lagrangians in dimension 2. Earlier this year, in collaboration with Riviere, we generalized this method to the case of Willmore energy, a conformally invariant Lagrangian whose critical points satisfy a geometric biharmonic equation in dimension 2. In this talk, we will first explain the method in the case of harmonic maps, then show how it applies to biharmonic maps in dimension 4 and the new technical difficulties that arise in this setting.

六、主讲人简介

Alexis Michelat，2019年博士毕业于苏黎世联邦理工学院(ETH Zurich)，师从著名数学家Tristan Riviere教授，现为洛桑联邦理工学院Bernoulli Instructor。主要研究方向为几何分析，在调和映照、Willmore曲面等方向做出了重要贡献，在Ann. Sci. Ec. Norm. Super., Arch. Ration. Mech. Anal., Comm. Anal. Geom., Cal. Var. PDEs等期刊发表论文多篇。

七、主办单位

非线性期望前沿科学中心

数学与交叉科学研究中心

中俄数学中心青岛基地