Quantum periods of orbifold del Pezzo surfaces

Recent work of Coates, Corti, Kasprzyk et al. investigated Mirror Symmetry for del Pezzo surfaces with isolated cyclic quotient singularities: on one side there are such surfaces with their quantum cohomology, whereas on the other side there are polygons and Laurent polynomials. In this talk, I will review a couple of conjectures in this field and I will provide some evidence for the case where the surfaces has only a particular type of singularity, based on joint work with Alessandro Oneto.