Exceptional structures in mathematics and physics from dynamics on graphs
Insights into Mathematics
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An introduction to a new course in the Explore Research Level Maths series, available to Members at the sister channel Wild Egg Maths. We want to explain a simple but powerful approach to ADE graphs, Coxeter graphs, Dynkin diagrams, root systems, simple Lie algebras, Weyl groups and associated geometry coming from the Tits quadratic form and extensions of all these ideas to general graphs.
The approach is through the remarkable Mutation game on populations on a graph. This video will provide an initial overview to these ideas meant especially for lay people and undergrads who do NOT have prior experience with Lie theory. We are wanting to explain a number of exceptional structures in mathematics, culminating in the E8 root system and its symmetries, but then extending to far more general graphs.
Along the way we will be looking a combinatorial structures that arise which play a key role in both representation theory and modern physics, particularly conformal field theory and string theory. We will also be touching base with ideas from the Wolfram physics project.
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Screenshot PDFs for my videos are available at the website http://wildegg.com. These give you a concise overview of the contents of the lectures for various Playlists: great for review, study and summary.
My research papers can be found at my Research Gate page, at https://www.researchgate.net/profile/...
My blog is at http://njwildberger.com/, where I will discuss lots of foundational issues, along with other things.
Online courses will be developed at openlearning.com. The first one, already underway is Algebraic Calculus One at https://www.openlearning.com/courses/... Please join us for an exciting new approach to one of mathematics' most important subjects!
If you would like to support these new initiatives for mathematics education and research, please consider becoming a Patron of this Channel at https://www.patreon.com/njwildberger Your support would be much appreciated.