一、報告題目

Morse Index Stability of Biharmonic 人林Maps in Critical Dimension

二、主講人

Alexis Michelat (瑞士洛桑聯邦在問理工(gōng)學院)

三、報告時(shí)間

2024年1月19日16：00 – 17:30

四、報告地點

Zoom會(huì)議号：929 633 3179務黃2

五、摘要

The Morse index of a cr雨煙itical point of a Lagrangian子為 is the dimension of the maximal vector場藍 space on which the second d信樂erivative is negative-definite. In the 靜雜classical theory, one shows t地畫hat the Morse index is 妹在lower semi-continuous, 資個while the sum of the Morse i車服ndex and nullity is upper semi用年-continuous.

Last year, Da Lio, Gianocca, an相哥d Riviere developed a new method to s道火how upper semi-continuity results i房要n geometric analysis—that they 間器applied to conformally invariant La但匠grangians in dimension 2. Earl女服ier this year, in co少美llaboration with Riviere, we g坐體eneralized this method to the case of W章什illmore energy, a co在年nformally invariant Lagrangia短一n whose critical points sati科上sfy a geometric biharmon哥笑ic equation in dimension 2. In this音地 talk, we will first廠日 explain the method in the case of為地 harmonic maps, then show how it ap如書plies to biharmonic maps in dimens雜在ion 4 and the new technical d資校ifficulties that arise in thi店放s setting.

六、主講人簡介

Alexis Michelat，2019年博士畢業于蘇黎世聯邦理工(機又gōng)學院(ETH Zurich)，師從著名數學家(jiā)Tris討市tan Riviere教授，現為(wèi)洛桑聯邦土樹理工(gōng)學院Bernoulli Instructor。主要空務研究方向為(wèi)幾何分析，在調和映照、Will近秒more曲面等方向做出了重要貢獻，在Ann. Sci. Ec. Norm. Super., Arch. Rat我費ion. Mech. Anal., Comm. Anal.玩家 Geom., Cal. Var. PDEs海國等期刊發表論文多篇。

七、主辦單位

非線性期望前沿科(kē)學中心

數學與交叉科(kē)學研究中心

中俄數學中心青島基地