Stable pointed curves and stable maps

In that talk, follow the section 2.1. of [5]. As in the book, take stacks as a black box (maybe you can give a rough idea about it: we like quotients to exists but the non-triviality of the stabilizer(s) is usually a problem for the quotient to exist as a scheme, hence we have to pass to stacks; in our case, the groups in questions are group of automorphisms2, passing to stacks will make more functors representable. Since things could seem a little hidden under the carpet here, put the emphasis on the examples and especially on the Gromov-Witten invariant since it will be important in the sequel: this is the object for curves counting and it comes into the play in the definition of quantum cohomology. Explain the manifestation of stacky phenomena in Gromov-Witten invariants (when they are not a natural number).