Geometric evolution problems in nonlinear partial differential equations

这个项目旨在解决对理解几何演化方程和某些其他非线性偏微分方程式至关重要的重要问题。要解决的问题存在于一个非常活跃的数学领域：调和映射、液晶和杨-米尔斯理论。特别的目的是开发新的方法来解决调和映射和杨-米尔斯方程中的公开问题，并通过著名的Ericksen-Leslie和Landau-de Gennes理论提高对实际问题的理解，例如液晶的数学建模。预期结果是数学中的基本结果，在其他科学中也有应用。

This project aims to address important problems key to the understanding of geometric evolution equations and certain other nonlinear partial differential equations. The problems to be tackled lie in a very active area of mathematics: harmonic maps, liquid crystals and Yang-Mills theory. Special aims are to exploit new methods to settle open problems in harmonic maps and Yang-Mills equations, and to improve understanding of practical questions such as the mathematical modelling of liquid crystals via the celebrated Ericksen-Leslie and Landau-de Gennes theories. The expected outcomes are fundamental results in mathematics, with applications in other sciences.