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Nonabelian Hodge Correspondence is a statement relating the world of algebraic topology (character varieties -- representations of $\pi_{1}(X)$), smooth geometry (flat bundles), and the holomorphic world (Higgs bundles), in particular, it is a surprising relationship which allows us to study wildly different structures with a large variety of techniques from the breadth of algebraic, smooth, and complex geometry. In this talk I will motivate the objects involved in the correspondence as interesting algebro-geometric objects to study in their own right then outline the Riemann-Hilbert Correspondence to relate the character variety $Hom(\pi_{1}(X),GL_{r}(\mathhbb{C})}$ with holomorphic vector bundles over $X$ with flat connections and the Nonabelian Hodge Correspondence to relate flat holomorphic vector bundles with Higgs bundles. 

Free pizzas as always:)