时间：2026年8月25日（周二）14:00-15:00
地点：E14-212
报告人：龚禹霖，University of Bristol
报告人简介：Yulin Gong is a Senior Research Associate at the School of Mathematics, University of Bristol, working with Dr. Laura Monk and Prof. Jens Marklof. He completed my Ph.D. at Tsinghua University under the supervision of Prof. Long Jin. His research interests include spectral theory on random hyperbolic surfaces and microlocal analysis.
报告主题：Uniform observability for Schrödinger equations on arbitrary Riemannian covers of closed negatively curved surfaces
报告摘要：In this talk, we study observability for the Schrödinger equation on arbitrary Riemannian covering spaces $\pi:X\to M$, where the base space $M$ is a closed negatively curved surface. Our main result shows that, for every time $T>0$, the Schrödinger equation is observable from the preimage $\pi^{-1}(\Omega)$ of any nonempty open subset $\Omega\subset M$, with a control constant $C(M,\Omega,T)$ that is uniform with respect to the covering map $(\pi,X)$.
The proof is divided into high-frequency and low-frequency regimes. In the high-frequency regime, we identify functions on $X$ with sections of flat Hilbert bundles over $M$. We then extend the long-time propagation and semiclassical control estimates of Dyatlov-Jin-Nonnenmacher to all unitary flat Hilbert bundles over $M$, with constants uniform in the choice of bundle. In the low-frequency regime, we combine the spectral inequality of Deleporte-Lagacé-Rouveyrol with an abstract observability inequality of Green-Kleinhenz to control the low-frequency remainder. This yields the desired observability inequality on $\pi^{-1}(\Omega)$. We will also discuss applications of the resulting uniform semiclassical control estimates to spectral geometry.
This is joint work with Xin Fu, Westlake University, and Yunlei Wang, Louisiana State University.
