**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.