题   目：Computational Discrete Global Geometric Structures

报告人：赵辉

单   位：可计算整体离散几何结构实验室

时   间：2025年9月13日  9：00

地   点：数学与统计学院一楼报告厅

摘   要：Global geometric structures are geometric objects residing on various fiber bundles over manifolds, with their types numbering in the hundreds. They are finer structures than topology.Computational discrete global geometric structure is a pioneering research field defined and established by Hui Zhao.It focuses on three key areas:1) developing and implemented algorithms for constructing diverse global geometric structures on discrete meshes to catch their global properties;2) visualizing global geometric structures;3) exploring the applications of these implemented algorithms across various technological domains.Researchers have successfully designed and implmented algorithms for several global geometric structures, including harmonic one-forms, harmonic foliations, holomorphic quadratic differentials, harmonic foliations with poles, meromorphic quadratic differentials, and discrete Calabi flows, among others.In this talk, the speaker will explain the context of computational discrete global geometric structure, several algorithms of them, and demonstrate the visulizations of structures.If time permits, the presentation will also cover the concept of research on super-structured quadrilateral meshes with controllable global quadrilateral arrangement, as well as its potential solutions to several technical challenges currently faced in CAD-CAE industrial software, such as isogeometric analysis, T-spline generation, finite element computation, and hexahedral mesh generation.

简   介：Dr. Hui Zhao, Chief Scientist, Laboratory of Computational Discrete Global Geometric Structures. Prior to this role, he served as a Visiting Scholar at the Harvard John A. Paulson School of Engineering and Applied Sciences (SEAS), a Visiting Scholar at the Yau Mathematical Sciences Center (YMSC) of Tsinghua University, a Research Assistant at the Beijing Yanqi Lake Institute of Applied Mathematics (BIMSA), and a Lecturer at the School of Software Engineering, Beijing University of Technology. He received his doctoral degree from the Institute of Software, Chinese Academy of Sciences (ISCAS).