I am interested both in thinking of neural networks as physical systems and in applying them to problems in science. Some recent work includes building neural networks that know about conformal symmetry and using ML to search for dualities in physics. 

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In the past I have worked on applications of generalized global symmetries, which are symmetry principles that enforce the conservation of extended objects (like strings). They provide powerful new tools to understand the phases of matter and dynamics with them. You can read my textbook for a simple introduction to the field.

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I have also worked extensively on holographic duality, which states that certain theories of quantum gravity are actually secretly quantum field theories (roughly, theories describing sets of interacting particles) in one dimension lower. 

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This is practically useful for computations in field theory: when the field theory is strongly coupled, the gravity theory is typically classical and easy to understand. Thus we can map a strongly-correlated quantum physics problem to a simple exercise in classical geometry.  ​Holographic duality may also be conceptually profound. It suggests that we can shed light on the deep mysteries of quantum gravity by studying (in principle) more well-defined problems of quantum field theory, though the required reorganization of the degrees of freedom is not yet understood.

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My papers on the arXiv are here.