Over a decade ago, Welschinger defined invariants of real symplectic manifolds of complex dimensions 2 and 3, which count pseudo-holomorphic disks with boundary and interior point constraints. Since then, the problem of extending the definition to higher dimensions has attracted much attention.

In the talk we will give some background on the problem, and describe a generalization -- open Gromov-Witten invariants -- of Welschinger's invariants with boundary and interior constraints to higher odd dimensions, using the language of $A_\infty$-algebras and bounding chains. The bounding chains play the role of boundary point constraints. If time permits, we will describe equations, a version of the open WDVV equations, which the resulting invariants satisfy. These equations give rise to recursive formulae that allow the computation of all invariants for $\mathbb{C}P^n$.

This is joint work with Jake Solomon.

No previous knowledge of any of the objects mentioned above will be assumed.

In the talk we will give some background on the problem, and describe a generalization -- open Gromov-Witten invariants -- of Welschinger's invariants with boundary and interior constraints to higher odd dimensions, using the language of $A_\infty$-algebras and bounding chains. The bounding chains play the role of boundary point constraints. If time permits, we will describe equations, a version of the open WDVV equations, which the resulting invariants satisfy. These equations give rise to recursive formulae that allow the computation of all invariants for $\mathbb{C}P^n$.

This is joint work with Jake Solomon.

No previous knowledge of any of the objects mentioned above will be assumed.

## Date:

Thu, 03/03/2016 - 15:30 to 16:30

## Location:

Manchester Building (Hall 2), Hebrew University Jerusalem