Abstract: This talk aims to advertise a pattern/phenomenon that has emerged in many different mathematical areas during the past decades but is not currently well-understood. I will begin with a broad overview of the Kahler packages (Poincare duality, Hard Lefschetz, and Hodge-Riemann relations) that appear in geometry, algebra, and combinatorics, from the classics of Lefschetz to the recent wo...
AbstractThe study of moduli spaces of hyperKahler manifolds and low dimensional cubic hypersurfaces is an active direction in algebraic geometry. Thanks to kinds of Torelli theorem, many moduli spaces can be realized as locally symmetric varieties of unitary type or orthogonal type. Hodge theory, birational geometry and arithmetic geometry converge in this topic. In this talk I will give a gene...
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