From Matroids via Moduli Spaces to Particle Physics

A matroid is a fundamental and actively studied object in combinatorics. Matroids generalize linear dependency in vector spaces as well as many aspects of graph theory.

Moreover, matroids form a cornerstone of tropical geometry and a deep link between algebraic geometry and combinatorics.

After a gentle introduction to matroids, I will present parts of a new OSCAR module for matroids through several examples. I will focus on computing the moduli space of a matroid which is the space of all arrangements of hyperplanes with that matroid as their intersection lattice.

Lastly, I will discuss diverse applications of this module in the fields of particle physics and algebraic geometry.