Enumerative invariants from categories

I will talk about certain categorical invariants that are purely algebraic, Gromov–Witten-like invariants associated with smooth, proper Calabi–Yau categories. In the case of Fukaya categories, these are expected to recover the Gromov–Witten invariants of the underlying symplectic manifolds. After a brief overview of the mirror symmetry background, I will discuss an operadic interpretation of the construction of these invariants. Time permitting, I will also talk about the steps needed to relate the categorical invariants with the geometric ones and report on some ongoing work in this direction.