Introduction to Non-abelian Hodge Theory

Explore the fundamentals of Simpson's correspondence in this research seminar lecture that generalizes classical Hodge theory by examining the relationship between complex local systems and semistable Higgs bundles with vanishing Chern classes on smooth projective varieties. Delve into the mathematical foundations that extend traditional Hodge theory into the non-abelian realm, understanding how this correspondence provides a bridge between differential geometry and algebraic geometry. Learn about the key concepts underlying this important area of mathematics through detailed explanations of the theoretical framework that connects topological and geometric structures in algebraic varieties.