Gromov-Witten invariants in Fano threefolds of index 2: some examples

In this talk, I explain one explicit formula for counting the number of rational curves passing through certain number of points in the 3-dimensional projective spaces $\mathbb{C}P^3$ (also called Gromov-Witten invariants in $\mathbb{C}P^3$) based on the paper of E.Brugallé and P.Georgieva. I also give the idea for computing GW invariants in two other types of Fano threefolds index 2 and claim a general formula.