中国科学院数学与系统科学研究院
数学研究所
数学科学全国重点实验室
学术报告
偏微分方程研讨班
Speaker: 李步扬 教授 (香港理工大学)
Inviter: 范晨捷
Language: English
Title: Finite element methods for isometric embedding of Riemannian manifolds
Time & Venue: 2026年3月20日（星期五）9：00-10：00 & 腾讯会议：229-511-339 密码：75223
Abstract: The isometric embedding problem for Riemannian manifolds, which connects intrinsic and extrinsic geometry, is a central question in differential geometry with deep theoretical significance and wide-ranging applications. Despite extensive analytical progress, the nonlinear and degenerate nature of this problem has hindered the development of rigorous numerical analysis in this area. As the first step toward addressing this gap, we study the numerical approximation of Weyl’s problem, i.e., the isometric embedding of two-dimensional Riemannian manifolds with positive Gaussian curvature into R³, by establishing a new weak formulation that naturally leads to a numerical scheme well suited for high-order finite element discretization, and conducting a systematic analysis to prove the well-posedness of this weak formulation, the existence and uniqueness of its numerical solution, as well as its convergence with error estimates. This provides a foundational framework for computing isometric embeddings of Riemannian manifolds into Euclidean space, with the goal of extending it to a broader range of cases and applications in the future. Our framework also extends naturally to the isometric embedding of the Ricci flow, with rigorous error estimates, enabling the visualization of geometric evolutions in intrinsic curvature flows. Numerical experiments support the theoretical analysis by demonstrating the convergence of the method and its effectiveness in simulating isometric embeddings of given Riemannian manifolds as well as Ricci flows.
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Speaker: 吴奕飞 教授（南京师范大学）
Inviter: 范晨捷
Language: English
Title: Second-order uniformly accurate method for the semiclassical nonlinear Schr\"odinger equation in $H^2$
Time & Venue: 2026年3月20日（星期五）10：00-11：00 & 腾讯会议：229-511-339 密码：75223
Abstract:
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