**Title:**Representation theory in graph theory

**Project Leaders:** David Hansen and Daniel Litt

**Abstract:** The goal of this project will be to study the linear-algebraic structures that arise naturally from certain combinatorial problems involving graphs. Classical results of Stanley and others allow one to deduce tricky combinatorial results from the representation theory of Lie algebras (for an example,
look here). This project will study the more complicated structures that arise from problems in graph coloring, the theory of graph minors, and so on, depending on students' interests. Comfort with linear algebra, and ideally some representation theory, is a prerequisite for this project.