Speaker: Alexis Michelat, Bernoulli Instructor, Swiss Federal Institute of Technology Lausanne

Date: January 19, 2024

Time: 16:00-17:30

Location: Zoom: 929 633 31792

Sponsor: Frontiers Science Center for Nonlinear Expectations, Shandong University; Research Centre for Mathematics and Interdisciplinary Sciences Centre, Shandong University; Sino-Russian Mathematics Center in Qingdao

Abstract:

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.

For more information, please visit:

https://www.view.sdu.edu.cn/info/1020/187068.htm