Quadratically enriched tropical intersections 2

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 second talk we define the quadratically enriched multiplicity at an intersection point of two tropical curves and show that it can be computed combinatorially. We will use this new approach to prove an enriched version of the Bézout theorem and of the Bernstein–Kushnirenko theorem, both for enriched tropical curves.

algebraic geometrycombinatorics

Audience: researchers in the topic

Tropical Geometry in Frankfurt/Zoom TGiF/Z

Series comments: Description: An afternoon seminar series on tropical geometry, known as the TGiZ ("Tropical Geometry in Zoom") or the TGiF ("Tropical Geometry in Frankfurt") seminar.

Please send an email to one of the organizers at the latest one day before a session if you wish to receive the Zoom link and password.

Videos of some past talks are available on YouTube here, while some slides can be found here.