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Explore a detailed lecture on the intermediate Jacobians of Gushel--Mukai varieties, delivered by Alexander Kuznetsov from the Steklov Mathematical Institute of Russian Academy of Sciences. Delve into the intricacies of Gushel--Mukai varieties, defined as smooth dimensionally transverse linear sections of a 6-dimensional intersection between the cone CGr(2,5) over Gr(2,5) and a quadric. Examine how the derived category of these varieties exhibits K3 type for even dimensions and curve-Enriques type for odd dimensions. Discover the description of intermediate Jacobians for GM threefolds and fivefolds as Albanese varieties of associated double EPW surfaces, and investigate the birational and categorical aspects of this phenomenon. Gain insights from collaborative research with Olivier Debarre and Alex Perry in this advanced mathematical exploration.
