The Ubiquity of ADE Graphs, and the Mutation and Numbers Games - Math Seminars

Explore the fascinating world of ADE graphs in this 51-minute math seminar lecture. Delve into the ubiquity of these remarkable graph structures across advanced mathematics and physics. Learn about the mutation and numbers games associated with ADE graphs, and discover their connections to Lie algebras, reflection groups, root systems, and more. Gain insights into the combinatorial methodology for creating structure from these graphs, and understand their significance in various fields, including quark theory and conformal field theories. Follow along as Prof. N J Wildberger from UNSW Sydney presents this intriguing topic, covering concepts such as spectral radius, eigenvalues, and the mysterious appearances of ADE graphs in diverse mathematical contexts.

Introduction
ADE Tilles
Why are they special
The Mutation Game
The Mutation
Example
The Group
The Game
Example 1e6
Theorem
Maximum Population
Proof of Ubiquity
Mutation Games
Roots
Positive Populations
Negative Populations
The E8