Eduard Balzin (Ecole Polytechnique)
Homotopical algebra and Cartesian fibrations
One important aspect of passing from "non-derived" to "derived" mathematics is the appearance of new and important objects which are algebraic and homotopic in their character. An example of such is the existence of an E_2-algebra structure on the Hochschild cochain complex, the statement which is otherwise known as Deligne conjecture.
In my talk I will sketch a way to think about homotopical algebraic structures, originally due to Segal, which relies on the machinery of Cartesian fibrations of (higher) categories. As an example of objects involved, we will speak of a couple of very concrete categories describing E_2-algebras, and mention a comparison result which can, among other things, be used to prove Deligne conjecture.