Title: Real Gromov-Witten Theory In Genus Zero and Beyond
Speaker: Mohammad Farajzadeh Tehrani, Princeton
Date: Thursday, May 30, 2013
Time: 1:30pm – 2:30pm
Place: Lecture Hall 102, Simons Center
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Abstract There are two types of $J$-holomorphic spheres in a symplectic manifold invariant under an antisymplectic involution: those that have a fixed point locus and those that do not. The former are described by moduli spaces of $J$-holomorphic disks, which are well studied in the literature. In this talk, we first study moduli spaces describing the latter and then combine the two types of moduli spaces to get a well-defined theory of counting real curves of genus 0. We then extend this idea to genus one to define real g=1 invariants and talk about the difficulties of generalizing this construction to higher genus. Using equivariant localization over odd dimension projective space, I will provide several examples in genus zero and one, supporting and explaining this construction.