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Topology prerequisite and Eric Weinstein's Geometric Unity!

Hello quantum enthusiasts,

It's looking more likely that the first prerequisite mini-series for the Lie Theory will be in June! The idea is to start with point-set topology using basic set-theoretic notions. Then we'll move on to metric spaces so we can construct the standard topology on R^n, where R is the set of reals. After this, we'll get into topological manifolds 101 and cover some basics of differentiable manifolds (aka smooth manifolds).

Because of the tight schedule, I'll assume you already have basic set-theoretic notions that we'll need. So I highly recommend that you review some basics of naive set theory including:

  •  Intersections and unions.

  • Cartesian products.

  • Maps between sets including; pre-images, composition, injectiveness, surjectiveness, bijection etc.

  • Indexing sets as well as their unions and intersections.

To help you review the basics of set theory, please check out the free study material for lecture #1 of the foundation module: (recommended focus on pages 80 - 115 and pages 157 - 196). The errata for the book can be found here.

Finally, I've recently received an interesting email from a community member asking whether she will be able to hack her way into understanding Eric Weinstein's 'Geometric Unity' (GU) paper after going through the Lie Theory module?! I've not read the paper nor intend to do so anytime soon until I can dive deeper into the physics side!:) However, Timothy Nguyen and a co-author released a response paper where they highlight technical gaps in GU (see here).

Anyway, you'll probably not be able to follow the technical subtleties of the GU paper with just the Lie Theory module. However, hopefully the module will give you a decent and relevant abstract group-theoretic foundational knowledge required for GU level. Likewise, on the geometric/topological side of things, you'll hopefully be able to have a basic understanding of manifolds that makes it easier to dive deeper into advanced topics in differential geometry/topology required to assess GU mathematically.

With this, I wish you a happy week!


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