From Matroids to Moduli Spaces

Explore the mathematical foundations and applications of matroids in this 56-minute lecture from the Geometry of Matroid Workshop at the Institute for Advanced Study. Begin with a foundational introduction to matroids before diving into demonstrations of a new OSCAR software module through practical examples. Learn about computing moduli spaces of matroids and understand how they relate to hyperplane arrangements and their intersection lattices. Discover the practical applications of this mathematical framework across diverse fields including particle physics, algebraic geometry, and theoretical computer science, showcasing the broad impact and utility of matroid theory in modern scientific research.