Exceptional structures in mathematics and physics from dynamics on graphs

Описание: We initiate a new Explore Research Level Mathematics course which shows how to develop a wide range of fascinating exceptional structures in mathematics and physics from the dynamics of two remarkable games on graphs: the Numbers Game of Mozes, which was motivated by an IMO problem by E. Wegert and the dual Mutation Game studied by us.

These games are intimately connected with Coxeter and Dynkin diagrams, with root systems, with Weyl groups and the classification of simple Lie algebras and also some exceptional finite simple groups. Remarkable lattices appear, as do quaternions, octonians and beyond, and we meet a rich new branch of combinatorics involving posets with rich structures.

Please join me on an epic adventure through a wide range of topics! These lectures will be accessible to Members of the Wild Egg Maths channel.

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.

************************
Gere are all the Insights into Mathematics Playlists:

Elementary Mathematics (K-6) Explained:    / playlist  
list=PL8403C2F0C89B1333
Year 9 Maths:    • Плейлист  
Ancient Mathematics:    • Плейлист  
Wild West Banking:    • Плейлист  
Sociology and Pure Mathematics:    • Плейлист  
Old Babylonian Mathematics (with Daniel Mansfield):    / playlist  
list=PLIljB45xT85CdeBmQZ2QiCEnPQn5KQ6ov
Math History:    • Плейлист  
Wild Trig: Intro to Rational Trigonometry:    • Плейлист  
MathFoundations:    • Плейлист  
Wild Linear Algebra:    • Плейлист  
Famous Math Problems:    • Плейлист  
Probability and Statistics: An Introduction:    • Плейлист  
Boole's Logic and Circuit Analysis:    • Плейлист  
Universal Hyperbolic Geometry:    • Плейлист  
Differential Geometry:    • Плейлист  
Algebraic Topology:    • Плейлист  
Math Seminars:    • Плейлист  
************************

And here are the Wild Egg Maths Playlists:

Triangle Centres:    • ENCYCLOPEDIA OF TRIANGLE CENTERS  
Six: An elementary course in pure mathematics:    • Плейлист  
Algebraic Calculus One:    • Плейлист  
Algebraic Calculus Two:    • Плейлист  
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.

***************
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   / njwildberger   Your support would be much appreciated.