TGiZ-Seminar: Tropical geometry in Zoom (First meeting Winter Semester 2022/23)

Sabrina Pauli (Universität Duisburg-Essen)

Abstract:
Tropical geometry has been proven to be a powerful computational tool in enumerative geometry over the complex and real numbers. Results from motivic homotopy theory allow to study questions in enumerative geometry over an arbitrary field k. In these two talks we present one of the first examples of how to use tropical geometry for questions in enuemrative geometry over k, namely a proof of the quadratically enriched Bézout’s theorem for tropical curves.

In the first talk we explain what we mean by the “quadratic enrichment”, that is we define the necessary notions of enumerative geometry over arbitrary fields valued in the Grothendieck-Witt ring of quadratic forms over k.