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Séminaire de Géométrie Ergodique

14h00-16h00 - Carlos Simpson (CNRS, Université Côte d’Azur)

"Nonabelian mixed Hodge structures"

Abstract: The space of representations of the fundamental group is a first nonabelian cohomological invariant, for which a rich “nonabelian Hodge theory” can be elaborated. We’ll discuss here the idea of how to use higher stack theory to de- fine similar invariants capturing information about higher homotopy groups of an algebraic variety. This will revisit the preprint math/0006213 with Katzarkov and Pantev, then expanding towards the relationship with twistor structures, perfect complexes, schematization of rational homotopy theory, and higher Tan- nakian categories.