Monoidal categories describe the "quantum symmetries" of 2-dimensional topological phases of matter.
Recently, it's been realised that enriched monoidal categories provide a useful model for 2-dimensional phases at the boundary of a 3-dimension phase. One of the simplest cases of a enriched monoidal category is a super monoidal category (it's a category enriched in super vector spaces, with a tensor product which interacts with the parity operator).
This project would involve learning about monoidal categories and super monoidal categories. It seems likely that several aspects of studying monoidal categories will actually be simpler for super monoidal categories, and the project may start investigating some of these.
(Required background: you should have seen the definition of a monoidal category before we start).