Opers and Non-Abelian Hodge: Numerical Studies

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We present numerical experiments that test the predictions of a conjecture of Gaiotto–Moore–Neitzke and Gaiotto concerning the monodromy map for opers, the non-Abelian Hodge correspondence, and the restriction of the hyperkähler L 2 metric to the Hitchin section. These experiments are conducted in the setting of polynomial holomorphic differentials on the complex plane, where the predictions take the form of conjectural formulas for the Stokes data and the metric tensor. Overall, the results of our experiments support the conjecture.