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An important problem in enumerative geometry is counting rational curves that interpolate a configuration of points in P^2, leading to Gromov-Witten invariants (over algebraically closed fields) and Welschinger invariants (over the real numbers). Recently, Kass, Levine, Solomon, and Wickelgren constructed "quadratic" invariants that work over an (almost) arbitrary base field. The “inconvenience” is that these new invariants are no longer numbers, but quadratic forms whose rank and signature recover the previously mentioned invariants. In a current work with Erwan Brugallé and Kirsten Wickelgren, we study these invariants in the framework of so-called Witt-invariants and show that, conversely, the quadratic invariants can be recovered from Gromov-Witten and Welschinger invariants. In my talk, I want to give an introduction to this topic (and its extension to rational del Pezzo surfaces).
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