20250612 Cisca Kalmijn

In this talk we will continue to explore the world of topological strings, specifically the A-twisted nonlinear sigma model (NLSM) as introduced by Jesse Straat on May 16th. The aim will be to actually compute the observables of a NLSM with a (smooth) toric variety as target. The trick will be to look at a so-called gauged linear sigma model (GLSM) whose low-energy limit is the NLSM we want. When studying the observables, we encounter the quantum cohomology ring, an extension of the ordinary cohomology, as a way of combining this information into a ring with product. It turns out that these observables are closely related to the Gromov–Witten invariants of classes corresponding to the operators we consider.

If time permits, we will look at a different formulation of quantum cohomology using the Gromov–Witten invariants directly.

Note that the talk will be accessible for both physicists and mathematicians that want to see such an approach to quantum cohomology.