Foundations of Matroids - Lecture 2

Explore a comprehensive lecture from the Institute for Advanced Study's Special Year Seminar II where Oliver Lorscheid delves into the foundations of matroids, building upon concepts from the first lecture. Learn about the structure theorem for foundations of ternary matroids, rooted in Tutte's homotopy theorem, and discover its implications for the representation theory of ternary matroids. Examine a concise proof of a folklore theorem about rigid matroid realization spaces, attributed to Laurent Lafforgue. Investigate the connection between Lorentzian polynomials and matroids over triangular hyperfields, leading to the resolution of Petter Branden's conjectures about the topological type of Lorentzian and stable polynomial spaces.