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Explore the theory of perverse coherent sheaves and their applications in algebraic geometry and geometric representation theory in this advanced mathematics lecture. Learn about Bezrukavnikov's coherent analog of perverse constructible sheaves, examining the two primary well-behaved examples: the nilpotent cone and the affine Grassmannian. Discover the connections between this category and modular representation theory, local geometric Langlands, line defects in 4d gauge theories, and cluster categorifications. Investigate a generalization of this construction to arbitrary Poisson varieties with finitely many symplectic leaves, with particular focus on symplectic singularities. Understand how this work represents progress toward developing Kazhdan-Lusztig theory in this mathematical setting, providing foundational knowledge for researchers working in algebraic geometry, representation theory, and related fields.
