(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.
