Joy Hamlin, "Hook Multiplication in the Quantum K-Theory Ring of the Grassmannian"

Description: Quantum K-theory is a formal deformation of K-theory that encodes Gromov-Witten invariants of the moduli space of curves meeting Schubert varieties in the Grassmannian. There are two Pieri rules, dual to each other, for multiplication in the quantum K-theory of a Grassmannian, but no positive formula for more complicated products is known. I will generalize both Pieri rules to find a complete description of the product when an arbitrary class is multiplied by a "hook class", involving a relation between quantum K-theory products with hook classes in different Grassmannians.