Real Gromov-Witten theory in all genera

Princeton/IAS Symplectic Geometry Seminar
Topic:Real Gromov-Witten theory in all genera
Speaker:Penka Georgieva
Affiliation:Institut de Mathématiques de Jussieu, Université Pierre et Marie Curie
Date:Friday, October 9
Time/Room:1:45pm - 2:45pm/Fine 322, Princeton University

We construct positive-genus analogues of Welschinger's invariants for many real symplectic manifolds, including the odd-dimensional projective spaces and the quintic threefold. Our approach to the orientability problem is based entirely on the topology of real bundle pairs over symmetric surfaces. This allows us to endow the uncompactified moduli spaces of real maps from symmetric surfaces of all topological types with natural orientations and to verify that they extend across the codimension-one boundaries of these spaces. In reasonably regular cases, these invariants can be used to obtain lower bounds for counts of real curves of arbitrary genus. Joint work with A. Zinger.