Luis Serrano
Hurwitz numbers and Lagrange's theorem
The Hurwitz problem consists of counting the n-sheeted branched covers of
the sphere up to a homeomorphism. This problem has a very combinatorial
nature, as it is equivalent to counting the number of factorizations of a
permutation in some special circumstances.
In this talk we will go through a bit of the history of the problem and
sketch the proof by Goulden and Jackson. The main tools will be Lagrange's
theorem, and the join-cut equation.