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Explore the powerful PDE tool of the Allen--Cahn equation and its application in studying minimal hypersurfaces in Riemannian manifolds in this 52-minute conference talk. Delve into important recent results, including the speaker's multiplicity-one theorem in three dimensions. Gain insights into the intersection of partial differential equations and geometric analysis as the talk focuses on minimal surfaces and their relationship to the Allen--Cahn equation, particularly in the context of 3-manifolds.
