Joint UNSW-USYD Seminar on Stochastic PDEs: Shengquan Xiang (Peking University) -- Wave maps

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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.