Carlos Simpson, University of Nice: Lefschetz devissage and Hodge theory

Carlos Simpson, University of Nice: Lefschetz devissage and Hodge theory Lefschetz proposed the study of the topology of complex algebraic varieties and gave a general method revolving around families of hyperplane sections. The topological invariants of the hyperplane sections vary in local systems over the base projective space, with singularities along the discriminant divisor, and the monodromy representations encode topological data. The fundamental group of the complement of the discriminant divisor thus plays a major role. This led to Griffiths' notion of variation of Hodge structure. Following the basic study of asymptotic properties of degenerations by Griffiths, Schmid, Clemens, Steenbrink, Cattani, Kaplan, Kashiwara, Kawai, Deligne, Saito and others, Zucker's theorem explains how to integrate the VHS coming from the Lefschetz pencil, to the Hodge-theoretic information of the original complex structure. This was generalized by Saito. These theories are inputs to the notion of nonabelian Hodge correspondence. We'll explore some recent aspects.