Andrea Petracci: On the quantum cohomology of a particular type of Del Pezzo surfaces

Recent work of Coates-Corti-Galkin-Kasprzyk uses quantum cohomology to reproduce the Iskovskikh-Mori-Mukai classification of smooth Fano 3-folds. The central idea is that the quantum period of a smooth Fano 3-fold corresponds to the classical period of certain Laurent polynomials supported on 3-dimensional reflexive polytopes. It is conjectured that a similar correspondence holds between del Pezzo surfaces with isolated quotient singularities and a certain class of Laurent polynomials supported on Fano polygons. In this talk I will show some examples of such a correspondence. This is joint work with Alessandro Oneto.