2025/26研资局研究学者计划得奖者 数学系
李文俊教授
数学系
香港中文大学
Biography
(只提供英文版)
- Associate Professor in Department of Mathematics at The Chinese University of Hong Kong
- Research interests include Geometric Analysis, Geometric Partial Differential Equations, General Relativity
- RFS project — aims to study the existence and regularity of minimal surfaces that arise naturally in the context of geometry, phase transition and general relativity. By employing novel variational methods and non-linear partial differential equation techniques, the research aims to give a mathematically rigorous construction of minimal surfaces and analyze their singularities using modern geometric analysis tools. This project will investigate how these surfaces evolve under physical laws and their impact on related fields like phase transitions, superconductivity and numerical relativity. The findings could help in visualizing, for example, how shapes change over time and how trapped surfaces are formed in space-time according to Einstein’s equation in general relativity.
- Awards and Honours:
- RGC Senior Research Fellow (2025)
- Hong Kong Mathematical Society Young Scholar Award (2021)
- NSFC Excellent Young Scientist Fund (2020)
Project Title
(只提供英文版)
- Minimal Surfaces in Geometry, Phase Transition and General Relativity
赞词
李文俊教授为香港中文大学数学系副教授。他是一位从事微分几何和偏微分方程研究的纯数学家。李教授的研究兴趣在于极小曲面理论的几何分析，以及它们在其他科学学科中的应用。他曾获得多项奖项和荣誉，例如国家自然科学基金优秀青年科学基金和香港数学会青年学者奖，以表彰他在这些领域的奠基性贡献。
本项目旨在研究几何、相变理论和广义相对论中自然产生的极小曲面的存在性和正则性。透过利用最前沿的变分方法和非线性偏微分方程等数学技巧以严格构造各种极小曲面，并且运用现代几何分析的工具来分析其奇异点性质。
是次研究将更深入探讨边界效应，对建构完整的极小曲面理论至关重要。本项目亦将运用最先进的技术，探讨这些曲面在物理定律下如何演化，以及它们对相变理论、超导体理论和数值相对论等相关领域的影响。这些发现将会有助于更清楚描述形状如何随时间变化，以及帮助我们了解爱因斯坦广义相对论中的视界如何在时空中演化等等物理上的重要应用。
