Abstract:
We introduce a signed count of real polynomials which gives rise to a real analog of Hurwitz numbers in the case of polynomials. The invariants obtained allow one to show the abundance of real solutions in the corresponding enumerative problems: in many cases, the number of real solutions is asymptotically equivalent (in the logarithmic scale) to the number of complex solutions.
This is a joint work with Dimitri Zvonkine.