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Recent Advances on Scalar Curvature Problems: June 27 – July 1, 2022

Organized by Alessandro Carlotto (Zurich), Marcus Khuri (Stony Brook), Philippe G. LeFloch (Paris), and Rafe Mazzeo (Stanford)

Problems involving the scalar curvature of a Riemannian manifold (prescribed curvature, existence, uniqueness, comparison, convergence, rigidity, regularity, etc.) arise in many areas of mathematics and physics. Over the past decade, there has been spectacular progress on such problems in several fronts in the mathematical research. Beyond their intrinsic relevance in Riemannian geometry, these questions also connect naturally to the description of gravitational forces in the context of general relativity. This workshop will be centered on recent developments on Einstein’s constraint equations, metrics with positive scalar curvature, static Einstein spaces, and mass and rigidity properties.