Analysis of fully non-linear geometric problems and differential equations

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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.