Linda Chen: Equivariant quantum cohomology of flag varieties, transversality and positivity

The enumerative geometry of homogeneous spaces has been studied since the nineteenth century: Schubert calculus describes the cohomology rings of Grassmannians and other flag varieties. Surprising relations between numbers of rational curves were established through quantum cohomology. I will describe the equivariant quantum cohomology of flag varieties. Some tools and consequences include the Quot scheme, equivariant transversality for spaces of maps, and positivity. This is joint work with Dave Anderson.