Maxim Kazarian
Steklov Math Inst RAS and Independent University of Moscow

Bouchard-Marino recursion fo Huwitz numbers

The Bouchard-Marino conjecture is a recursion for Hurwitz numbers enumerating ramified coverings of the sphere. A proof of this conjecture was given recently by B. Eynard, M. Mulase, and B. Safnuk. In the talk we undertake a revision of this proof in the framework of the Chekhov-Eynard-Orantin theory. We show that the Bouchard-Marino conjecture becomes a reformulation of the known cut-and-join equation for Hurwitz numbers and its proof requires essentially no involved computations. Besides, we derive a new recursion for Hurwitz numbers which are close but not identical to that of Bouchard and Marino.