Over a decade ago, Welschinger defined real enumerative invariants in dimensions 2 and 3. It has remained an open problem to extend these invariants to higher dimensions. I will discuss a solution to this problem in the language of open Gromov-Witten theory. The key idea is that boundary point constraints should be replaced with canonical gauge equivalence classes of Maurer-Cartan elements (bounding chains) in the relevant Fukaya A-infinity algebra. The resulting invariants satisfy a version of the open WDVV equation, which determines all invariants for projective spaces. Conjugation symmetry does not place an essential role in our arguments.

This is joint work with S. Tukachinsky. Speaker(s): Jake Solomon (IAS)