Mathematics Colloquia and Seminars

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Galois discovered that solving a polynomial equation defined on a given field is equivalent to construction of field extensions, and the nature of these field extensions are encoded in the groups acting on the roots of polynomials. When we start with a field of meromorphic functions on a Riemann surface, the vision of Galois leads us to geometry of moduli spaces of Higgs bundles, representation varieties of surface groups, hyperkahler geometry of holomorphic symplectic manifolds, and category of D-modules. I will present some of the new excitements on this subject, using a concrete picture of Lagrangian fibrations.