Lukas Kühne: Computing the moduli space of a matroid and applications to hyperplane arrangements

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.   Later, I will discuss its applications in the realm of hyperplane arrangements. First, I will outline a connection between matroid realization spaces, operators that act on line arrangements, and elliptic modular surfaces. Time permitting, I will discuss line arrangements with only triple intersection points.