Non-abelian Hodge theory, as developed by Hitchin and Simpson, establishes a correspondence between local systems (topological objects) and Higgs bundles (holomorphic objects) on compact Kaehler manifolds. It was extended to the complex quasi projective manifolds by T.Mochizuki.
The goal of this course will be to present this correspondence, and its corollaries for the topology of Kaehler manifolds. For instance, SL(n, Z) is not the fundamental group of a compact Kaehler manifold.
Prerequisite: basics of complex geometry, algebraic geometry, Hodge theory.
- Course owner: Bruno Klingler
Semester: SuTerm 2022