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Blowing-up the edge: connection formulae and stability chart of the Lam\'e equation
Giulio Bonelli, Pavlo Gavrylenko, Tommaso Pedroni, Alessandro Tanzini
https://arxiv.org/abs/2507.04860

Blowing-up the edge: connection formulae and stability chart of the Lamé equation
We study periodic spectral problems through their connection with supersymmetric gauge theories and two-dimensional conformal field theory. To characterize the associated stability chart, we develop a novel and systematic approach for analyzing semi-classical Virasoro blocks near their poles. Via the AGT correspondence, these blocks correspond to SU(2) Nekrasov partition functions in the Nekrasov-Shatashvili limit, which we propose to resum using an appropriate limit of blow-up equations. We sh…