Mirror symmetry for Lagrangian Grassmannians (joint with K. Rietsch)
Clélia Pech (Université Lyon 1)
Monday 26th January, 2015 16:00-17:00 Maths 204
In this talk I will explain how to construct a mirror for Lagrangian Grassmannians (i.e. Grassmannians of Lagrangian vector subspaces of a symplectic vector space). This mirror will take the shape of a rational function, the superpotential, defined on a (Langlands dual) orthogonal Grassmannian. This mirror possesses interesting properties. In particular, the mirror manifold has a particular combinatorial structure called a cluster structure, and the superpotential is expressed in coordinates dual to the cohomology classes of the Lagrangian Grassmannian LG(n).
I will also explain how these properties lead to new relations in the quantum cohomology of LG(n), and a conjectural formula expressing solutions of the quantum differential equation for LG(n) in terms of the superpotential. If time allows, I will also explain how these results should extend to a larger family of homogeneous spaces called `cominuscule homogeneous spaces'.