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John Baez (Jul 15 2020 at 06:11):Here are some things I wrote that might be interesting to some:
1) We all love duality, but what's "triality"?.
Duality is a big theme in mathematics. Triality is more exotic. Any vector space has a dual. But a triality can happen only in certain special dimensions! (1/n) https://twitter.com/johncarlosbaez/status/1283066917251461120/photo/1
- John Carlos Baez (@johncarlosbaez)
John Baez (Jul 15 2020 at 06:14):2) The most symmetrical Riemannian manifolds: "symmetric spaces".
A Riemannian manifold is, roughly speaking, a space in which we can measure lengths and angles. The most symmetrical of these are called "symmetric spaces". In 2 dimensions there are 3 kinds, but in higher dimensions there are more. (1/n) https://twitter.com/johncarlosbaez/status/1281965979744927745/photo/1
- John Carlos Baez (@johncarlosbaez)
John Baez (Jul 15 2020 at 06:16):3) A quick intro to Jordan algebras.
Jordan algebras are fascinating to me - but annoying. The usual definition uses the "Jordan identity", which looks completely random. With help from @gro_tsen I found an equivalent definition that says more about what's good about Jordan algebras. (1/n) https://twitter.com/johncarlosbaez/status/1277274080123576320/photo/1
- John Carlos Baez (@johncarlosbaez)