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Explore Koszul Duality on quantizations of bionic symplectic varieties in this advanced mathematics lecture by Gwyn Bellamy from the University of Glasgow. Delve into localization theorems à la Beilinson-Bernstein and their application to representations of quantizations of symplectic singularities. Examine the equivalence between these representations and modules over sheaves of deformation-quantization algebras on symplectic resolutions. Investigate the application of these concepts to spherical rational Cherednik algebras, finite W-algebras, and primitive central quotients of enveloping algebras. Learn about the construction of a "local generator" in geometric category O and its role in establishing an equivalence between the bounded derived category of coherent DQ-modules and the derived category of coherent modules over the dg-endomorphism ring. Understand how this work generalizes the classical D-Omega duality and represents an example of filtered Koszul duality. Gain insights into recent collaborative research with Chris Dodd, Kevin McGerty, and Tom Nevins in this hour-long M-Seminar presentation at Kansas State University.
