Equivariant Gromov-Witten theory and GKM spaces

Abstract: An important class of examples in algebraic and symplectic geometry is given by GKM spaces, which are torus-equivariant spaces with finitely many fixed points and complex-one-dimensional orbits. This class includes smooth toric varieties, homogeneous spaces, smooth Schubert varieties, as well as many non-algebraic examples like the twisted flag manifold of Eschenburg/Tolman/Woodward.

At the intersection of geometry, algebra, and combinatorics lies a fruitful two-way interaction between Gromov-Witten theory and GKM theory established by equivariant localization. In one direction, GKM theory provides a setting where Gromov-Witten invariants become explicitly computable, which we have implemented in a software package (joint work with Giosuè Muratore). In the other direction, the axiomatic behavior of Gromov-Witten invariants is strong enough to imply structural properties of GKM spaces. I will present recent results in both directions.

mathematical physicsalgebraic geometryalgebraic topologydifferential geometryrepresentation theorysymplectic geometry

Audience: researchers in the topic

Geometry and Physics @ Lisbon