Maximal Mumford Curves and Graph Embeddings in Real Algebraic Geometry

Learn about embedded stable curves over real numbers and their relationship to hyperplane arrangements in this mathematics lecture from the Institute for Advanced Study. Explore how the connected components of a hyperplane arrangement's complement correspond to embeddings of stable curve graphs on compact surfaces, and understand how surface topology influences real deformation types. Delve into the connection between graph curves and maximal Mumford curves (MM-curves), discovering the crucial relationship between graph planarity and MM-curve special fibers. Based on collaborative research with Bernd Sturmfels and Raluca Vlad, gain insights into advanced mathematical concepts at the intersection of algebraic geometry and graph theory.