On the Frobenius manifold from the Gromov–Witten theory for an orbifold projective line with $r$ orbifold points

In this talk, I will explain the Frobenius structure on the orbifold quantum cohomology ring of an orbifold projective line with $r$ orbifold points. In particular, I will show that this Frobenius structure can be determined by certain initial conditions. This result should be the key theorem to show that this Frobenius structure is isomorphic to the (conjectural) Frobenius structure constructed from the invariant theory of the corresponding extended cuspidal Weyl group.