Covering semigroups and irreducible components of Hurwits spaces

In the talk, I'll introduce a semigroup structure on the set of marked degree $d$ coverings of oriented surfaces (spheres with handles) with a given Galois group embedded into the symmetric group $S_d$. As an application, the number of irreducible components of Hurwitz space of marked degree $d$ coverings of a projective curve with fixed ramification type will be counted in terms of the Galois group and the set of local monodromies of coverings if the number of brunch points of the coverings is big enough.