GT seminar: "A universal characterization of uncurving"

Abstract: Given a curved A-infinity algebra and a bounding cochain (a.k.a Maurer-Cartan element), one can twist the former by the latter to get a new A-infinity algebra where the curvature is zero. This uncurving procedure plays a central rôle in Floer theory, where Fukaya categories are naturally curved objects. The goal of this talk will be to give a universal characterization of the procedure, using the theory of operads: we will show that the operad cMC, whose algebras are curved A-infinity algebras endowed with a Maurer-Cartan element, together with its natural morphism to the A-infinity operad, is terminal in a certain comma category. This category does not contain the Maurer-Cartan equation, thus the theorem provides a way to « rediscover » it as the answer to a universal algebraic problem. This is joint work with Adrian Petr and Vivek Shende.

This is a talk in the geometry and topology seminar series.