Analysis of fully non-linear geometric problems and differential equations

该项目旨在研究非线性几何演化方程，这些方程在过去几十年中通过用于解决数学中的突出问题而受到相当大的关注，例如庞加莱猜想。通过开发创新的几何和分析交织的新技术，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，如双曲几何，以及材料科学中晶体生长中形成的不规则性的几何方法，重点是开发尖端的数学工具和几何连接。

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.