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Quantization and a conjecture of Gaiotto on opers

Mathematical Physics & Probability

Speaker: Motohico Mulase, Department of Mathematics
Location: 1147 MSB
Start time: Wed, Oct 9 2019, 3:10PM

Through his work on supersymmetric gauge theory in 4 dimensions, physicist Gaiotto conjectured in 2014 a mechanism of constructing "opers" from "spectral curves" via scaling limit. The conjecture itself has been solved in my joint paper with Dumitrescu, Fredrickson, Kydonakis, Mazzeo, and Neitzke. Dumitrescu and I then realized that the scaling limit construction is exactly what we have been looking for: a mathematical definition of "quantum curves" introduced by physicists Aganagic, Dijkgraaf, Hollands, Klemm, Marino, Sulkowski, and Vafa. In this talk I will first introduce quantum curves, discuss Gaiotto's conjectural formula, and then present most general mathematical theorems coming out of his conjecture.