New directions in geometric flows. A geometric flow describes how an object's shape evolves under applied forces, such as a bubble floating through air or a rubber band returning to its natural shape

Description

New directions in geometric flows. A geometric flow describes how an object's shape evolves under applied forces, such as a bubble floating through air or a rubber band returning to its natural shape by releasing bending energy. In this process, factors like area, volume, and curvature are optimised within given constraints. This project will explore two groundbreaking geometric flows: Sobolev curvature flow and the target flow, both specifically designed to build on the candidate's recent breakthroughs. Now is the perfect moment to drive forward transformative progress on two renowned open mathematical problems: the Cartan-Hadamard conjecture and a challenge posed by Fields Medallist S. T. Yau. Key benefits include new knowledge and research capacity building.. Scheme: ARC Future Fellowships. Field: 4904 - Pure Mathematics. Lead: Dr Glen Wheeler