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Gromov-Witten theory in genus zero.

In 2003 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.聽

In the talk, we give background on the problem and describe some previous approaches. We then formulate a result generalizing Welschinger's invariants with boundary and interior constraints to all odd (complex) dimensions. The resulting invariants satisfy a family of equations, called the WDVV equations. For $mathbb{C}P^n$, these equations allow the computation of all invariants. This is joint work with Jake Solomon.