19/05/2025, 14:00 — 15:00 —
Room P3.10, Mathematics Building
Miguel Barata, Utrecht University
An introduction to operads and operadic right modules
An operad P is a multivariable generalization of a category, first studied by Boardman, Vogt and May in the context of homotopy theory, where one allows for morphisms to have multiple inputs. The internal composition of P will encode some type of algebraic structure - such as an associative multiplication or a Lie bracket - and left actions by P will endow objects in a category with this extra algebraic information - thus defining associative monoids and Lie algebras in the previous examples. The operadic viewpoint has been of central importance in recent years in the world of highly-coherent algebra, but its influence has spread out to other areas of mathematics, such as mathematical physics, algebraic geometry and differential geometry.
In this talk I want to discuss what happens when operads act on the right instead, which leads to the notion of an operadic right module. The homotopy theory of such actions has had a revival in the last few years due to its connections to the Goodwillie-Weiss calculus of embedding spaces, which I hope to explain if time permits.
