Exceptional Structures in Mathematics and Physics From Dynamics on Graphs

Explore the fascinating world of exceptional structures in mathematics and physics through a 35-minute lecture on dynamics on graphs. Delve into the Numbers Game of Mozes and the dual Mutation Game, uncovering their connections to Coxeter and Dynkin diagrams, root systems, Weyl groups, and the classification of simple Lie algebras. Discover remarkable lattices, quaternions, octonions, and a new branch of combinatorics involving posets. Gain insights into the E8 root system, its symmetries, and extensions to general graphs. Examine combinatorial structures crucial to representation theory and modern physics, including conformal field theory and string theory. Designed for lay people and undergraduates without prior Lie theory experience, this overview touches on ideas from the Wolfram physics project and provides a foundation for understanding exceptional mathematical structures.