Count of meanders on surfaces of higher genera. REPORTE

(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 higherthan zero.