A construction of open-closed categorical enumerative invariants

Starting with a cyclic A-infinity category, this talk constructs enumerative invariants with both open and closed sectors. The approach extends Costello's closed-sector construction through appropriate differential graded Lie algebras and trivializations of circle actions. Applications include a unital, cyclic version of the Bogomolov–Tian–Todorov theorem and a construction of quantum A-infinity algebras. The presentation describes ongoing joint work with Lino Amorim.