# Peter Spacek: Mirror symmetry for cominuscule homogeneous spaces

**Time: **
Fri 2020-12-04 14.00 - 14.45

**Location: **
Zoom, meeting ID: 657 9019 8929

**Participating: **
Peter Spacek, Kent

### Abstract

The strength of mirror symmetry is the ability to translate between two theories to use the advantages of both. We will be considering mirror symmetry for the (small) quantum cohomology, which is a deformation of the cohomology using Gromov-Witten invariants as structure constants. For homogeneous spaces, mirror symmetry tells us that the quantum cohomology is isomorphic to a polynomial ring with relations. In fact, the ring arises as the coordinate ring of a subvariety of the Langlands dual homogeneous space, and the relations are all obtained as the derivatives of a single function on this subvariety, called the potential. I will present a local Laurent polynomial expression for this potential that holds for all cominuscule homogeneous spaces and that can be stated type-independently. We will illustrate these concepts and results on small examples.

**Zoom Notes: **The meeting ID is 657 9019 8929 and the passcode is 3517257.