Koszul Duality on Quantizations of Bionic Symplectic Varieties

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.