Dirac electrons’ sea, Hurwitz theory, and quantum curves.

In the last talk we have seen how Hurwitz numbers have a representation theoretic expression. This formulation can be used to express them further as operators shuffling around Maya diagrams defined on Dirac electrons’ sea. This have deep consequences at the level of integrable hierarchies (but we will see it in detail only in a future talk). On the other hand, these operators turn out handy for computational purposes. In particular, there is a way to derive quantum curves…