报告题目：Towards Computational Topological (Magneto)Hydrodynamics: long term computation of fluids and plasma

报告人：胡凯博 牛津大学副教授、高级研究员

报告时间：2025年12月22日 10：30

报告地点：数学楼天元研讨室五

报告摘要: From Kelvin and Helmholtz to Arnold, Khesin, and Moffatt, topology has drawn increased attention in fluid dynamics. Quantities such as helicity and enstrophy encode knotting, topological constraints, and fine structures such as turbulence energy cascades in both fluid and MHD systems. Several open scientific questions, such as corona heating, the generation of magnetic fields in astrophysical objects, and the Parker hypothesis, call for topology-preserving computation.

In this talk, we investigate the role of topology (knots and cohomology) in computational fluid dynamics by two examples: relaxation and dynamo. We investigate the question of “why structure-preservation” in this context and discuss some recent results on topology-preserving numerical analysis and computation. Finite Element Exterior Calculus sheds light on tackling some long-standing challenges and establishing a computational approach for topological (magneto)hydrodynamics.

报告人介绍：胡凯博，现任牛津大学副教授、高级研究员及皇家学会大学研究员。主要研究方向包括相容与保结构离散、有限元外微分、计算拓扑流体力学，以及离散几何、拓扑及其应用。

2012年于南开大学获学士学位，2017年于北京大学获博士学位。其后先后在挪威奥斯陆大学和美国明尼苏达大学从事博士后研究，2021—2023年任牛津大学Hooke研究员，后任爱丁堡大学副教授（Reader）。

2023年获SIAM计算科学与工程早期职业奖，2024年获欧洲研究委员会启动基金（ERC Starting Grant)。其文章入选SIAM高影响力文章合集（2023）、ICBS前沿科学奖（FSA, 2025），并获多项其他论文奖。