Wave maps from circle to Riemannian manifold: global controllability is equivalent to homotopy

讲座题目：Wave maps from circle to Riemannian manifold: global controllability is equivalent to homotopy 
讲座时间 Datetime: 2025年9月26日，周五，16:15-18：30
地点 Venue: 腾讯会议：518-786-752
主持人 Host：黄山林 教授
报告人 Speaker:向圣权 助理教授
单位 Affiliation: 北京大学 
报告摘要 Abstract:
We study wave maps from the circle to a general compact Riemannian manifold. We prove that the global controllability of this geometric equation is characterized precisely by the homotopy class of the data. As a remarkable intermediate result, we establish uniform-time global controllability between steady states, providing a partial answer to an open problem raised by Dehman, Lebeau and Zuazua (2003). Finally, we obtain quantitative exponential stability around closed geodesics with negative sectional curvature. This work highlights the rich interplay between partial differential equations, differential geometry, and control theory. Based on a recent joint work with Jean-Michel Coron and Joachim Krieger.
报告人简介：
向圣权，北京大学数学科学学院助理教授。2015年获北京大学学士学位，2017年获巴黎高等师范学院硕士学位，2019年获法国索邦大学博士学位。其主要研究方向为偏微分方程控制、随机动力系统。在SIAM J. Control, ESAIM: COCV, JMPA, Arch. Ration. Mech. Anal., Anal. PDE, Ann. Inst. H. Poincare C, JFA, JDE等杂志发表论文若干篇。