Why the Hall conductance is quantized was an open problem in condensed matter theory for much of the past 40 years. Spyridon Michalakis who worked on the solution — published in 2015 — gives a personal take on how the field evolved.
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Aizenman’s list of open problems in mathematical physics: http://web.math.princeton.edu/~aizenman/OpenProblems_MathPhys/
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Michalakis, S. Why is the Hall conductance quantized?. Nat Rev Phys 2, 392–393 (2020). https://doi.org/10.1038/s42254-020-0212-6
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DOI: https://doi.org/10.1038/s42254-020-0212-6
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