We will present a type-independent construction of mirror models for the small quantum cohomology of cominuscule homogeneous spaces, in joint work with Charles Wang.
Cominuscule homogeneous spaces are a kind of projective varieties with transitive actions of algebraic groups that include many well-known examples, such as quadrics, Grassmannians, and Lagrangian Grassmannians. One of their distinguishing properties is the fact that their Langlands dual homogeneous spaces allow an embedding into the projectivization of a minuscule representation, i.e. a representation in which the weights form a single orbit under the Weyl group. This embedding allows us to use the combinatorics of minuscule posets to construct mirror models in explicit projective coordinates type-independently, where previous constructions depended on the specific representation theory of the algebraic group.