SPEAKER: Bruno Valette
TITLE: How to use Manin's products to prove Deligne's conjecture for Loday algebras with Koszul property
ABSTRACT In this talk, we will give a conceptual definition of Manin products in any category endowed with two coherent monoidal products. This construction can be applied to associative algebras, non-symmetric operads, operads, colored operads, and prop(erad)s presented by generators and relations. These two products, called black and white, are dual to each other under Koszul duality functor. These products allow us to define natural operations on the chain complex defining cohomology theories of algebras. With these operations, we are able to prove that Deligne's conjecture holds for a general class of operads and is not specific to the case of associative algebras. Finally, we prove generalized versions of a few conjectures raised by M. Aguiar and J.-L. Loday related to the Koszul property of operads defined by black products. These operads provide infinitely many examples for this generalized Deligne's conjecture.