Sabrina Pauli (Düsseldorf)

Abstract: Results from motivic homotopy theory allow to study questions in enumerative geometry over an arbitrary field k. In this case the answer to these questions is not a number but a quadratic form carrying arithmetic information about the count. Using tropical geometry one can translate questions from enumerative geometry to questions in combinatorics which are often easier to solve. In my talk I will present one of the first examples of how to use tropical geometry for questions in enumerative geometry over an arbitrary field k, namely a proof of Bézout’s theorem for tropical curves. This is joint work with Andrés Jaramillo Puentes.