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Explore the final installment of a three-part lecture series on perverse coherent sheaves and their applications to symplectic singularities. Delve into Bezrukavnikov's coherent analog of perverse constructible sheaves, examining the two primary well-behaved examples: the nilpotent cone and the affine Grassmannian. Discover how these categories connect to modular representation theory, local geometric Langlands, line defects in 4d gauge theories, and cluster categorifications. Learn about the generalization of this construction to arbitrary Poisson varieties with finitely many symplectic leaves, particularly focusing on symplectic singularities as a foundation for developing Kazhdan-Lusztig theory in this mathematical framework.
