Reading Group on Mirror Symmetry by Examples

I will describe the non-homological (i.e. enumerative) aspect of mirror symmetry for a particular toric Calabi-Yau 3-fold, the total space of the canonical bundle over $\mathbb P^2$. In this case, there is a simpler B-model on its mirror curve which predicts all genus Gromov-Witten invariants. I will also describe the global Kahler moduli space and discuss the relation to $\mathbb C^3/\mathbb Z_3$ via mirror symmetry.