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研究员，博士生导师。2015年本科毕业于北京大学数学与应用数学专业，同年获法国巴黎七大数学专业硕士学位，2017年获法国巴黎高师文凭，2019年获法国索邦大学应用数学专业博士学位。2019-2022年在瑞士洛桑联邦理工学院从事博士后研究。研究方向为控制论与偏微分方程，包括几何映射的控制流、色散方程与定量控制、定量快速镇定等。论文发表于Journal de Mathématiques Pures et Appliquées，SIAM J. Control Optim.等。