Analysis of fully non-linear geometric problems and differential equations

这个项目旨在研究在过去几十年中通过使用非线性几何演化方程来解决数学中的突出问题，例如庞加莱猜想，这些方程受到了相当大的关注。通过开发将几何和分析相互交织在一起的创新新技术，该项目致力于在模拟复杂现象的非线性问题方面取得进展。该项目涉及各种主题，从双曲几何到材料科学中晶体生长中形成的不规则的几何方法，重点是开发尖端的数学工具和与几何的联系。

This project aims to investigate non-linear geometric evolution equations that have received considerable attention in the past decades through their use in solving outstanding problems in mathematics, such as the Poincare conjecture. By developing innovative new techniques intertwining geometry and analysis, the project endeavours to make advances in non-linear problems modelling complex phenomena. The project addresses topics as varied as hyperbolic geometry, and a geometric approach to irregularities forming in crystal growth in materials science, focusing on developing cutting-edge mathematical tools and connections to geometry.