## 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.