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Explore Nash's C^1 isometric embedding theorem and the Borisov-Gromov problem in this comprehensive lecture by Camillo De Lellis, part of the Infosys-ICTS Ramanujan Lectures series. Delve into Nash's groundbreaking 1950s construction of C^1 isometric embeddings of Riemannian manifolds as hypersurfaces in Euclidean space. Examine the open Borisov-Gromov problem concerning the threshold Hölder regularity for the Nash phenomenon and its connection to the Onsager conjecture. Learn from De Lellis, a renowned mathematician and IBM von Neumann Professor at the Institute for Advanced Study, as he shares insights on calculus of variations, geometric measure theory, and fluid dynamics. This 1 hour 53 minute lecture, delivered at the International Centre for Theoretical Sciences, offers a deep dive into advanced mathematical concepts for researchers and enthusiasts in the field.
