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Explore geometric variational problems and their heat flows in this mathematics colloquium talk delivered by Yannick Sire from Johns Hopkins University. Delve into techniques for addressing existence, regularity, and singularity formation in various geometric problems inspired by harmonic map variations, Yang-Mills connections construction, and nematic liquid crystals. Discover recent advancements in constructing fine asymptotics of blow-up solutions through a novel gluing method designed for parabolic flows. Gain insights into open problems and potential generalizations in this field, emphasizing the flexibility of the discussed techniques.
