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Quantization of Hitchin's spectral curves and "opers"

QMAP Seminar

Speaker: Motohico Mulase, UC Davis, Math. Dept
Location: 2112 MSB
Start time: Thu, Jan 14 2016, 3:10PM

The goal of the talk is to explain a conjecture by D. Gaiotto on the relation between Higgs pairs, Hitchin's equations, and "opers". The conjecture has been recently solved in a joint work by Dumitrescu-Fredrickson-Kydonakis-Mazzeo-Mulase-Neitzke. In this talk I will focus on the holomorphic geometry side of the story, which gives an extremely simple and concrete description of opers. Here, opers are the mathematical counterpart of physicists' notion of "quantum curves". I will explain how the Planck "constant" comes into the deformation theory of complex structures as a parameter of a sheaf cohomology group. The analysis side of the story will be discussed by Laura Fredrickson of UT Austin in our String Theory Seminar in May.