A Graphical Approach to Higher Cyclic and Modular Operads

We give an introduction to the cyclic and modular operads of Getzler and Kapranov, and indicate graphical categories which are suitable for controlling up-to-homotopy versions of these. Cyclic operads are a variation on operads where the distinction between input and output of operations is relaxed, while modular operads additionally allow for self-gluing of operations.

This talk is based on joint work with Marcy Robertson and Donald Yau. It would be helpful to have some familiarity with categories and functors, but prior knowledge about operads is unnecessary.