报告题目：Singular Structures and Generic Regularity of Minimal Surfaces and Mean Curvature Flow

时间：2025年12月18日（周四） 下午3:00

地点：清华大学文北楼102会议室

报告人：Zhihan Wang（Cornell University，Klarman fellow）

摘要：Singularities arise naturally in geometric variational problems and evolution equations. A fundamental question is to understand the local structure of these singular sets, both in general settings and under generic assumptions. In this talk, I will discuss recent progress on the analysis of singularities for the area functional, focusing on structural results and generic regularity phenomena in minimal surfaces and mean curvature flow.

报告人简介：Zhihan Wang is a Klarman fellow at Cornell University. He obtained his Ph.D. from Princeton University in 2023 under the supervision of Fernando Marques. His research centers on geometric variational and evolution problems.

王志涵是康奈尔大学Klarman研究员，2023年于普林斯顿大学获得博士学位，导师为Fernando Marques。他的研究专注于几何变分与演化问题。

报告题目：Complexity of manifold optimization

时间：2025年12月18日（周四） 下午4:00

地点：清华大学文北楼102会议室

报告人：赖泽华（University of Texas at Austin, Austin, TX）

摘要：This talk presents both complexity-theoretic and geometric perspectives on optimization over matrix manifolds, including the Stiefel, Grassmannian, flag, orthogonal, and positive-definite manifolds. I will explain why many fundamental optimization problems on these spaces are NP-hard. A unifying theme behind these results is that the diagonal images of these manifolds encode rich combinatorial structure, enabling reductions from classical problems such as clique number, max-cut, and stability number. In the second part of the talk, I will discuss geometric complexity measures associated with these manifolds, focusing on their Euclidean distance degrees and condition numbers. Together, these results connect discrete complexity, algebraic geometry, and differential geometry in the study of manifold optimization.