Geometric Graph Theory - Weyl Groups, Root Systems and Quadratic Forms

This course explores the geometry of graphs through the Mutation Game, generating special populations forming root systems. It introduces Weyl/Coxeter groups, reflections, and symmetric bilinear forms. The course teaches how every graph provides a geometrical structure on its populations and a group of reflections, with a focus on A_n diagrams and the Mutation Game's role in representations. The teaching method involves theoretical explanations and examples. This course is intended for individuals interested in geometric graph theory, combinatorial games, and algebraic structures.