Analysis and Mathematical Physics

In spite of tremendous progress in the mean-field theory of spin glasses in the last forty years, culminating in Giorgio Parisi’s Nobel Prize in 2021, the more “realistic” short-range spin glass models have remained almost completely intractable. In this talk, I will show that the ground states of short-range spin glasses are chaotic with respect to small perturbations of the disorder, settling a conjecture made by Daniel Fisher and David Huse in 1986. The proof proceeds by converting the physics problem into a problem in analysis. Most of the major questions in the field, however, remain open. I will outline a general plan for converting these questions to problems in analysis, and pose them to the analysts in the audience.