quantum field theory and its interactions with geometry... "quantum geometry" if you will. Happy to go into detail... but y'know, twitter has its limits.
Only surfacing now because a long-running project has just about finished 
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Replying to @DanielleFong @raeez
i started doing my notes on an infinite canvas and explored a lot of fractal geometry when I stumbled upon william thurston's expositions on 3-manifolds and the geometrization conjecture. i started looking into computational physics on 3 manifoldspic.twitter.com/UA2zxuh4Ia
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Replying to @DanielleFong
the world of 3 manifolds is a beautiful and particularly rewarding garden to explore exactly those questions!
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Replying to @raeez
yes there's SO MUCH THAT YOU CAN DO with 3 manifolds it's been super underexploited. Poincare's theorem means that certain forms of dynamics can be thought of as computation on 3 manifolds that won't get caught, & the Ricci Flow method Perlman used to prove it gives the method
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Replying to @DanielleFong @raeez
the geometrization conjecture is fucking wild -- that you can break *any* 3-manifold (which as a physicist I think of as a 3d embedding) into just a few different fundamental architectures - it's mind bending & I think it's a great entry point into physicshttps://www.youtube.com/watch?v=o6SucT2Zzys …
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Replying to @DanielleFong
in recent times, that understanding has translated into a kind of lego-like decomposition of arbitrary quantum field theories!
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Replying to @raeez
so my idea is to do this with computational domains for my AR-over-the-world project.
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Replying to @DanielleFong @raeez
@raeez can you send me some of your fav papers on this I'd love to read what the state of the art is on this from the active frontier in mathematical physics.1 reply 1 retweet 2 likes -
Replying to @DanielleFong
will do. I'll have to think of a good sequence that's both accessible and gets at the essential ideas—stay tuned
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