Speaker: Konstanze Rietsch (KCL)
Title: Grassmannians, Mirror Symmetry and Polytopes

Abstract: Together with Robert Marsh we wrote down a mirror 'superpotential' W_q for a general Grassmannian and showed that W_q encodes the quantum cohomology of the original (A-model) Grassmannian and related structures. The superpotential is a function defined on a certain (B-model) cluster variety lying inside another Grassmannian. In this talk I will report on joint work with Lauren Williams which gives a different perspective on the same superpotential and illustrates the duality between the two Grassmannians. In this work we show that a set of polytopes constructed in the B-model using the tropicalisation of the superpotential on a cluster torus gives a Newton-Okounkov polytope. This Newton-Okounkov polytope is associated to particular divisor in the original (A-model) Grassmannian and a 'network torus' there, which we think of as being dual to the original cluster torus.