Seminar Room 2, Newton Institute Gatehouse
AbstractThere is a plethora of operad type structures and constructions which arise naturally in classical and quantum contexts such as operations on cochains, string topology or Gromov-Witten invariants.
We give a categorical framework which allows us to handle all these different beasts in one simple fashion. For instance operads, cyclic operads, modular operads, and other new types. In the enriched case, this also covers twisted modular operads, giving a natural description of hyper-operads. In this context, many of the relevant constructions are simply Kan extensions.
We are also able to show how in this framework bar constructions, Feynman transforms, master and BV equations appear naturally