Title: Higgs bundles and moduli spaces of sheaves on symplectic surfaces

Speaker: Riccardo Carini

Abstract: Higgs bundles on a Riemann surface Σ were first introduced by Hitchin in the 80’s in the study of Yang-Mills self-duality equations. Their moduli spaces are a natural partial compactification of the cotangent space of the moduli space of bundles on Σ, making them an interesting object of study in the realm of holomorphic symplectic geometry.
Via the spectral correspondence, they are closely related to moduli spaces of sheaves on symplectic surfaces, which currently represent the primary source of compact hyperkähler manifolds known to us. I will explore the relation between these moduli spaces, showing how they fit together in a nice one-dimensional family and both admit a very geometric Lagrangian fibration.

Some snacks will be provided before and after the talk.

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