Families of Hitchin systems and N=2 theories

Abstract: Over the last few years, the connection between 4d N=2 theories and Hitchin systems has led to a robust exchange of ideas between physics and mathematics. In my talk, I will explain how to extend this dictionary to one between 4d N=2 physics and the SL_N Hitchin system on a nodal UV Curve. I will then use this dictionary to clarify certain questions concerning Coulomb branches of the corresponding Class S theories at various boundaries of the space of marginal parameters. In mathematical terms, I will describe tame SL_N Hitchin systems as a flat family of integrable systems over \bar{M}, the Deligne-Mumford moduli space of the UV Curve. This is based on upcoming work with J. Distler and R. Donagi.

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