On the Non-abelian Hodge Correspondence for Higher-dimensional Quasiprojective Varieties

Explore the non-abelian Hodge correspondence for higher-dimensional quasiprojective varieties in this 34-minute research seminar talk. Examine Simpson's foundational work demonstrating a homeomorphism between the moduli space of semisimple flat bundles and polystable Higgs bundles with vanishing Chern classes on projective varieties. Delve into recent advances by Bakker, Brunebarbe and Tsimerman, who established a version of this homeomorphism for log smooth curves and achieved a continuous bijection for higher-dimensional log smooth varieties. Learn about the speaker's approach to extending this result, including a detailed argument for obtaining a full homeomorphism in arbitrary dimensions. Gain insights into the monodromy of Lagrangian fibrations as part of this advanced mathematical exploration presented at the Institute for Advanced Study's Special Year Research Seminar.