Count of meanders on surfaces of higher genera.

(joint work with V. Delecroix, E. Goujard and P. Zograf)

I  will  introduce  square-tiled surfaces and will explain why they
represent  integer  points  in  the  moduli  spaces  of Abelian and
quadratic  differentials.  I  will also give a hint on why count of
square-tiled  surfaces provides Masur-Veech volumes of these moduli
spaces.  I  will  show how count of square-tiled surfaces allows to
count meanders and orientable meanders on surfaces of genera higher
than zero.