The aim of the workshop is to bring together junior and senior researchers in character varieties and Hodge theory, and explore the connections between these two subjects. The workshop will consists of 7 introductory talks of 2.5 hours, as well as 4 research talks of 1 hour.
Abstract
Character varieties of surface groups are rich geometric objects lying at the intersection of topology, representation theory, and complex geometry. This workshop explores character varieties through the lens of Hodge theory, with a particular emphasis on complex variations of Hodge structures and their incarnation via nonabelian Hodge theory. Beginning with an introduction to polarized complex variations of Hodge structures, the workshop develops the correspondence between Hodge-theoretic data, Higgs bundles, and surface group representations. We will investigate how the C*-action on Higgs bundle moduli spaces detects representations arising from variations of Hodge structures, leading to geometric and dynamical applications to character varieties of closed and punctured surfaces. Topics include branched hyperbolic structures, compact components of relative character varieties, Hodge groups and their classification, and rigidity phenomena such as the Corlette–Simpson alternative. The workshop aims to make Hodge-theoretic techniques accessible while highlighting recent advances and open problems at the interface of Hodge theory and character varieties.
Registration and official website
Venue
Max Planck Institute for Mathematics Leipzig, Germany
Program
Organisers
Samuel Bronstein (MPI-MIS)
Arnaud Maret (Strasbourg University)