Résumé de l'exposé
It is nowadays trendy to count not any more with positive integers (as complex people do) nor with integers (as real people do), but with quadratic forms. This talk will address the problem of enumerating rational curves in algebraic surfaces from this quadratic point of view. I will give a conjectural expression of these geometric quadratic invariants only in terms of Gromov-Witten and Welschinger invariants. In other words quadratic invariants over any field should be determined by the two special fields C and R. This is a joint work with Johannes Rau and Kirsten Wickelgren.