Algebra/Topology Seminar by Eduard Balzin

Algebra/Topology seminar by Eduard Balzin (Nice)

Title: Segal approach for algebraic structures

Abstract: The operads are considered today as a conventional tool to describe homotopy algebraic structure. However, for the original problem of delooping, another formalism exists, bearing the name of Segal. This approach has proven advantageous in certain situations, such as, for example, modelling higher categories.

In this talk, I will present a generalisation of Segal formalism using operator categories of Barwick, and the language of Grothendieck fibrations, which is necessary to deal with the general monoidal structures. An application of our approach includes re-proving Deligne conjecture without any mention of operads, which, I hope, may convince you that Segal formalism can be used to produce interesting examples of factorisation algebras.