Explore the concept of enumerative invariants derived from categories in this M-Seminar lecture from Kansas State University. Delve into Kontsevich's suggestion that enumerative predictions of Mirror Symmetry can be directly inferred from Homological Mirror Symmetry. Examine two approaches to constructing analogues of Gromov-Witten invariants associated with dg or A-infinity Calabi-Yau categories: categorical primitive forms, a non-commutative version of Saito's theory for singularities, which provides genus zero invariants; and Costello's enumerative invariants, which potentially offer invariants across all genera. Gain insights into advanced mathematical concepts and their applications in Mirror Symmetry and category theory during this hour-long presentation by Lino Amorim.