Abstract:

Motivic homotopy theory allows us to tie together the results from classical and real enumerative geometry, and yield invariant counts of solutions to geometric questions over an arbitrary field k. The enumerative counts are valued in the Grothendieck-Witt ring GW(k) of non- degenerate quadratic forms over k and we call it quadratic enrichment. In this talk, I will detail some examples of these counts and I will present a quadratically enriched version of the Bernstein–Khovanskii–Kushnirenko theorem, as well as a quadratically enriched version of the Correspondence Theorem for counting curves passing through configurations of k- rational points.