ADE Graphs and Lattices, Weights and Quarks

Explore the fascinating world of ADE graphs and their connections to lattices, weights, and quarks in this one-hour lecture. Delve into the remarkable ubiquity of ADE graphs in mathematics, examining their relationships with optimal lattices for packing and kissing problems in dimensions 1 to 8, with a focus on the exceptional E8 lattice. Learn about the Numbers game on graphs, its duality to the Mutation game, and how these concepts relate to weights and populations on graphs. Discover the intriguing links between these mathematical structures and particle physics, including the representation theory of SU(2) and the eight-fold way that led to the discovery of quarks. Gain insights into the foundations of the standard model of particle physics and its connections to the A2 diagram, offering a unique perspective on the intersection of pure mathematics and fundamental physics.

Introduction
Lattices
Best lattices
What are lattices
The firing game
The weights
The numbers game
Flavor symmetry
Linear symmetry
Quarks
Color symmetry