The Moduli Space of Matroids - Lecture 1

Explore a comprehensive mathematics lecture that delves into F1-geometry and its connections to tropical geometry, matroid theory, Lorentzian polynomials, buildings, and cluster algebras. Designed for a general audience, learn about Baker-Bowler's theory of matroids with coefficients and discover how scheme theory can be defined using exotic algebraic objects called bands. Examine the construction of Grassmannians over F1 as moduli spaces of matroids, and understand how residue fields of these moduli spaces influence matroid representation theory. Through collaborative work with Matthew Baker, June Huh, Mario Kummer, and others, gain insights into a unifying framework that bridges multiple mathematical disciplines. Study practical applications through simple examples that demonstrate how structural analysis of these invariants leads to significant results in matroid representation theory.