The Ubiquity of ADE Graphs, and the Mutation and Numbers Games | Math Seminars | NJ Wildberger

This is the first of a series of lectures on a remarkable family of graphs called the ADE graphs, which figure, rather mysteriously, in many areas of advanced mathematics and physics.

Our aim will be to establish a simple combinatorial methodology for creating structure from these graphs, moving towards connections with Lie algebra and Lie groups, reflection or Coxeter groups, root systems, lattices, quivers, large simple groups, von Neumann algebras and maybe even some physics such as the theory of quarks, fusion rule algebra / hyper groups, and conformal field theories.

This talk was given in the Concrete Mathematics Seminar at UNSW in May 2018 by Prof N J Wildberger of the School of Mathematics and Statistics, UNSW Sydney. Many thanks to Sean Gardiner and Joshua Capel for videoing the lecture.

Small correction: When I mention the largest eigenvalue of a graph X, I say "spectrum" where I should have said "spectral radius", ie sp(X).

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[dwaynestammer]

Prof Wildberger posses the rare combination of being brilliant and good at communicating. His entire collection of videos is high quality.

[codebeard]

Thanks Prof Wildberger, I hope you can upload the rest of the series on this

[josh]

Thanks for this clear and interesting lecture. Math is a lifelong hobby for me, and this starts to cover some things I've been curious about for a while.

[robnicolaides]

Excellent talk, and very interesting object, thanks Norm. Is there a bijection between reduced words of the longest element in the group (maybe up to inverses) and root populations? Where can I learn more?