Geometry Seminar

Date: October 27, 2014

Time: 3:00PM - 4:00PM

Location: BLOC 624

Speaker: Jeremy Daniel, Institut de mathématiques de Jussieu

Title: Hodge Theory and Harmonic Bundles

Abstract: Hodge theory is a powerful tool to study the connections between the topological and the complex geometrical aspects of a complex projective manifold. The main idea is that these two kinds of invariants should meet in the harmonic structures attached to the manifold. I will explain this general principle, first in the classical (or Abelian) setting when one studies the de Rham and Dolbeault cohomologies of the manifold and then in the non-Abelian setting, when one is interested to the representations of the fundamental group and the Higgs bundles of the manifold. If time allows, I will speak of the meta-theorem of Simpson relating variations of Hodge structures and harmonic bundles and give a new light on this principle.