Abstract: A matroid is a fundamental and actively studied object in discrete mathematics. 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 matroid moduli spaces in the fields of particle physics, algebraic geometry, and theoretical computer science.
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