Résume | Usual Hurwitz numbers count the number of covers over CP^1 with a fixed ramification profile over point \infty and simply ramified over a specified set of points. They also can be treated as a weighted count of factorizations in the symmetric group. It is known, that Hurwitz numbers can be calculated via intersection indices on the moduli spaces of complex curves by so-called ELSV-formula.
In my talk, I will discuss monotone Hurwitz numbers, which also arise as factorizations count with restrictions. It turns out, that they also can be related to the intersection indices on the moduli spaces of complex curves. I will give a definition of monotone Hurwitz numbers, and try to explain the origin of the monotone ELSV. If time permits, I will speak about the further development of the subject.
The talk is based on the joint work with Norman Do (Monash University). |