Joana Cirici: Formality of symmetric monoidal functors and operads via mixed Hodge theory

ABSTRACT: I will recall the notion of formal lax symmetric monoidal functor and its direct implications to the study of operads and their formality. Then, I will prove an abstract result of "purity implies formality" in this setting. I will apply this result to show that, when restricted to complex algebraic varieties whose weight filtration in cohomology satisfies a certain purity property, the functor of singular chains with rational coefficients is formal. I will end with some examples and direct applications to the formality of operads arising from algebraic geometry. This is joint work with Geoffroy Horel.