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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the relationship is quite intricate... there's strong argument to be made that "classical" topology of 3-folds is intrinsically quantum, as things simplify only once you recognize the importance of 3d Topological Quantum Field Theory (i.e. topological phases of matter)
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also see an argument of: it's a computational universe, how do you make sense of it? well, by renormalization from any perspective. can renormalize almost boundlessly around any 0-d singularities (and strings) because of the the geometrization conjecture but the result is quantum
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on the other hand, quantization seems best understood as the deformation of something "commutative" to something "non-commutative"... there the most natural explanation of the "weirdness" falls out.
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yes. in my mind this is isomorphic to non-abelian, choosing a branch cut, generation of entropy, arrow of time. certain facts, events, shared, simultaneous state in history is irreversible in a sense
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Then you're led to ask what non-commutative deformations correspond to 3-fold topology... and the waters get pretty deep quite fast
There's a pretty deep connection, happy to explain it as I see it some time -
yeah so that's a fascinating question, right? it's not clear there are limits. following from the free will theorem, it's possible that an extremely willful and intelligent electron could play a sort of... extremely intelligent game of quantum go at the boundaries





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