Aiming to resolve Perelman’s conjecture, the authors and collaborators initiated a research program to study the classification of ancient solutions to geometric flows under natural geometric conditions. This article describes some of the main classification results, starting from the heat equation on manifolds and ending with three-dimensional Ricci flow.
In some sense, diffusion bears the idea of averaging, which in turn should imply a smoothing effect of the entity being averaged. Regularity theory is the mathematical manifestation of such an event, and keeping precise track of the estimates reveals important features of the model.
Liouville quantum gravity surfaces are defined as random topological surfaces equipped with a measure, a metric, and a conformal structure. They have a rich geometric structure that is still not fully understood.
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AMS President Jill Pipher to Congress: "No Longer Secure: Cryptography in the Quantum Era"
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Your Favorite Field a Superpower?
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