CORDIS Project
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This project aims to advance the understanding of geometric and topological problems by addressing singularities in mathematical models. It focuses on proving key theorems related to area-minimizing surfaces and curvature flows.
Major advances in geometry and topology have been achieved by studying critical points and gradient flows for natural energies, but these analytic methods are hindered when singularities occur.
In fact, singularities are the main obstacle in the use of area minimisation in the proof of the positive mass theorem up to dimension 7 and the use of Ricci flow with surgery in the proof of the 3-dimensional Poincaré conjecture. A key observation in geometry and physics is that generic solutions, obtain…
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