TGiF-Seminar: Tropical geometry in Frankfurt (First meeting Summer Semester 2024)

Lukas Kühne (Universität Bielefeld)

Abstract: A matroid is a fundamental and widely studied object in combinatorics. Following a brief introduction to matroids, I will showcase parts of a new OSCAR module for matroids using several examples. My emphasis will be on the computation of the realization space of a matroid, which is the space of all hyperplane arrangements that have the given matroid as their intersection lattice.

In the second part, I will discuss an application in the realm of algebraic geometry, namely a novel connection between matroid realization spaces and the elliptic modular surfaces.