Louis-Clément Lefèvre will speak on

Mixed Hodge structures and representations of fundamental groups of complex algebraic varieties

Abstract: Mixed Hodge structures, introduced by Deligne, are additional structures on the cohomology groups of complex algebraic varieties. They are important tools in the study of their topology and of their moduli. Since then, mixed Hodge structures have been constructed on other topological invariants of complex varieties, by Morgan and Hain. In this vein, we construct mixed Hodge structures on certain invariants associated to linear representations of the fundamental group. The starting point is the theory of Goldman and Millson, that relates this to the theory of formal deformations via differential graded Lie algebras. We review this using more modern tools, L-infinity algebras.