Vassily Gorbounov: Schubert calculus, quantum integrable systems and networks on surfaces

There are three counting problems — the intersection of the Schubert cycles in the Grassmannians, the boundary partition functions in quantum integrable systems and boundary measurements in networks on surfaces.

We will describe all three and show that there is a situation when all three count the same quantity. This implies that this quantity inherits some interesting properties which we will describe as well.