Mixed Hodge Structures on Cohomology Jump Ideals

Explore a 57-minute conference talk on Mixed Hodge Structures on Cohomology Jump Ideals, presented by Louis-Clément Lefèvre from Lycée Hoche, Versailles. Delve into the formal local ring in the representation variety of Kähler manifolds, first described by Goldman and Millson. Examine the construction of mixed Hodge structures on these local rings at representations given by the monodromy of variations of mixed Hodge structures, and their extension to non-compact varieties. Investigate cohomology jump ideals within the formal local rings, which locally define the locus of representations with dimensions constraints on their cohomology groups. Discover the speaker's goal of demonstrating that these ideals are sub-mixed Hodge structures, offering insights into the complex interplay between algebraic geometry and Hodge theory.