Speaker: Lino Amorim  (Kansas State University)

Abstract: Kontsevich suggested that enumerative predictions of Mirror Symmetry should follow directly from Homological Mirror Symmetry. This requires a natural construction of analogues of Gromov-Witten invariants associated to any dg or A-infinity Calabi-Yau category (with some extra choices). I will discuss two approaches to this construction: 1) categorical primitive forms, a non-commutative version of Saito's theory of primitive forms for singularities, which gives only genus zero invariants; 2) Costello's enumerative invariants which conjecturally give invariants in all genera.