# Algebraic Geometry Seminar

#### Extension of Welschinger'S Invariants Counting J-Holomorphic Discs to Higher Dimensions

**Speaker:**
Sara Tukachinsky, Hebrew University of Jerusalem

**Location:**
Warren Weaver Hall 905

**Date:**
Thursday, October 22, 2015, 3 p.m.

**Synopsis:**

Over a decade ago, Welschinger defined invariants of real symplectic manifolds of complex dimension 2 and 3, which count J-holomorphic disks with boundary and interior point constraints. Since then, the problem of extending the definition to higher dimensions has attracted much attention. We generalize Welschinger's invariants with boundary and interior constraints to all odd dimensions using the language of A_{∞} -algebras. The geometric structure of our invariants is expressed algebraically in a version of the open WDVV equations. These equations give rise to recursive formulae which allow the computation of all invariants for CP^{n}. This is joint work with Jake Solomon.