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Explore the monodromy properties of Lagrangian fibrations in this 35-minute research seminar from the Institute for Advanced Study. Delve into the higher-dimensional analogs of K3 surfaces through compact hyperkähler manifolds and examine how Lagrangian fibrations serve as generalizations of elliptic fibrations. Learn about Voisin's fundamental result demonstrating that these fibrations produce irreducible real variations of weight one Hodge structures. Discover the speaker's new findings proving that when the variation is not isotrivial, its underlying local system maintains irreducibility over the complex numbers. Gain insights into advanced topics in algebraic geometry, particularly the intersection of hyperkähler geometry, Hodge theory, and monodromy representations, presented as part of the Special Year Research Seminar series.
