TGiF-Seminar: Tropical geometry in Frankfurt (Second meeting Summer Semester 2023)

Roberto Gualdi (Regensburg)

Abstract:

Motivated by the computation of the integral of a piecewise linear func- tion on the amoeba of the line (x1 + x2 + 1 = 0), we will show how tropical objects play a role in arithmetics.

This will bring us to an excursion into the Arakelov geometry of toric varieties; in this framework, we will use our tropical computation to predict the arithmetic complexity of the intersection of a projective planar line with its translate by a torsion point. This is a joint work with Martín Sombra.