2025/26研資局研究學者計劃得獎者 數學系
李文俊教授
數學系
香港中文大學
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
讚詞
李文俊教授為香港中文大學數學系副教授。他是一位從事微分幾何和偏微分方程研究的純數學家。李教授的研究興趣在於極小曲面理論的幾何分析，以及它們在其他科學學科中的應用。他曾獲得多項獎項和榮譽，例如國家自然科學基金優秀青年科學基金和香港數學會青年學者獎，以表彰他在這些領域的奠基性貢獻。
本項目旨在研究幾何、相變理論和廣義相對論中自然產生的極小曲面的存在性和正則性。透過利用最前沿的變分方法和非線性偏微分方程等數學技巧以嚴格構造各種極小曲面，並且運用現代幾何分析的工具來分析其奇異點性質。
是次研究將更深入探討邊界效應，對建構完整的極小曲面理論至關重要。本項目亦將運用最先進的技術，探討這些曲面在物理定律下如何演化，以及它們對相變理論、超導體理論和數值相對論等相關領域的影響。這些發現將會有助於更清楚描述形狀如何隨時間變化，以及幫助我們了解愛因斯坦廣義相對論中的視界如何在時空中演化等等物理上的重要應用。
