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Explore a joint project relating coherent sheaves on a Springer fiber to microlocal sheaves on an affine Springer fiber for the dual group in this hour-long lecture by Roman Bezrukavnikov from MIT. Delve into the local counterpart of mirror duality between parabolic Hitchin spaces, examining the collaboration with Michael McBreen and Zhiwei Yun. Gain insights into this complex mathematical topic, which connects various areas of algebraic geometry and representation theory.