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Attend this comprehensive workshop exploring the intersection of geometric measure theory and optimal transport theory through expert lectures and collaborative learning. Delve into regularity theory for area-minimizing currents across six detailed sessions, examining the mathematical foundations and advanced techniques used to understand minimal surfaces and their properties. Explore optimal transportation theory and its connections to Monge-Ampère equations, discovering how these concepts relate to Riemannian geometry and Ricci curvature bounds through three progressive lectures. Master the fundamentals of optimal transportation and Monge-Ampère type equations in three introductory sessions designed to build your theoretical foundation. Investigate stability results for geometric inequalities through three focused presentations that demonstrate how small perturbations affect geometric properties. Study metric currents, isoperimetric inequalities, and compactness theory in three sessions that bridge measure theory with geometric analysis. Gain insights from leading researchers in the field while participating in discussions that connect theoretical developments to current research problems in geometric analysis and optimal transport.
