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Explore advanced topics in algebraic geometry through this research seminar that examines the relationship between isomonodromic deformations of flat bundles and the codimension of Hodge loci. Learn about establishing lower bounds on the codimension of components within the non-abelian Hodge locus as they exist within leaves of the isomonodromy foliation on the relative de Rham moduli space of flat vector bundles on algebraic curves. Discover how these bounds emerge from more general constraints on the rank of flat vector bundles where the Hodge filtration remains stable throughout isomonodromic deformation processes. Understand the extension of these bounds to flat vector bundles that do not underlie variations of Hodge structures, providing a generalization of the Landesman-Litt result. Gain insights into the intersection of differential geometry, algebraic geometry, and the theory of moduli spaces through this specialized mathematical presentation delivered as part of the Institute for Advanced Study's Special Year Research Seminar series.
