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Title:
Conformal limits and Morse vs. Oper stratifications
Speaker:
Abstract:
The notion of a conformal limit was introduced by Gaiotto to describe the behavior of solutions to the TBA equations under a certain scaling limit. In terms of moduli spaces, Gaiotto conjectured that the conformal limit provides a diffeomorphism between the Hitchin component in the Higgs moduli space and the space of opers in the de Rham moduli space. This conjecture was proven 2016 by Dumitrescu, et. al. The goal of these lectures will be to describe recent joint work with B. Collier in which we generalize this correspondence to give an identification of (nearly) the entire Morse and partial oper stratifications of the Hitchin and de Rham spaces. Along the way, I will give a complete proof of the existence of conformal limits for almost all Higgs bundles.
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