Update Feb 182023

Dear Patrons,

I would like to say hello and bring you up to speed with some of the things I am thinking about these days. Of course I am working on the various YouTube series that I've posted on recently: the Box Arithmetic videos in the Math Foundations series (also called Multiset Arithmetic) and the Explorations with q-series, and the Mathematics and Music series. In that last vein we are going to meet shortly a really rather peculiar alternative to our usual decimal conventions that I think will take you by surprise, and it's particularly curious coming from the "musical" background.

I am also working on further videos in the Dynamics on Graphs series, which is going to start getting very rich as we connect with both physics, combinatorics and algebra. The physics is in the direction of the Standard Model re quarks etc while the combinatorics is that of partially ordered set (posets) and associated lattices, while the algebra has to do with Weyl character formulas and Lie algebra representation theory.

This latter topic is a hugely interesting and important area of 20th century mathematics, which I have long been fascinated with. Its a challenge though to bring this material into view for amateurs without a big detour through the arcane world of Lie groups and associated differential geometry and harmonic analysis.

It turns out that this topic is also very important for quantum mechanics (QM), and indeed it has long been one of my aims to try to elucidate the connections between the physics of QM and certain mathematical manifestations of "quantization" which have been developed somewhat separate but parallel to the physics. In this direction I am going to shortly be starting another series called "Classical to Quantum" which I hope you find interesting.

As for my my own current research, it is a long-standing project of mine to understand explicitly the irreducible representations of simple Lie algebras. In fact I view this as pretty well the most important problem in modern pure mathematics. Its something I have been thinking about for at least 25 years, and now that I am retired I can focus more on it. Some of the developments tie in really well with both the Dynamics on Graphs lectures, the Diffusion Symmetry Lectures, and this upcoming Classical to Quantum series. So I hope to be telling you about some interesting aspects of this beautiful theory in the months ahead.

There are also some fantastic new formulas in the Algebraic Calculus direction that I have been developing with Sony Chan (RUPP in Cambodia) and I hope to bring those to your attention also before the end of the year.

And my former PhD student Kevin Limanta (UNSW) has been making great progress in integration formulas over spheres and other quadrics, also with higher dimensional extensions. I will want to be explaining some of that. Turns out that we can do a lot of the classical stuff without transcendental functions or constants: the core formulas are completely rational. And it all connects beautifully with classical combinatorics! :)

All the best, and thanks again for your continuing support.

Norman