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Explore advanced concepts in algebraic geometry and geometric representation theory through this mathematical seminar lecture delivered by Ilya Dumanski from MIT. Delve into the theory of perverse constructible sheaves and their coherent analog, perverse coherent sheaves, as introduced by Bezrukavnikov. Examine the two primary well-behaved examples of this notion: the nilpotent cone and the affine Grassmannian, understanding their significance in 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, with particular focus on symplectic singularities. Discover how this work represents a step toward building Kazhdan-Lusztig theory in this mathematical setting, connecting various areas of modern algebraic geometry and representation theory.
