Irregular opers, Stokes geometry and WKB analysis

Abstract: We study, using the extended isomonodromy deformation, the WKB approximation of Stokes matrices of a class of meromorphic linear ODE systems of Poincare rank 1 on the projective line that appear in various contexts of geometry. We show that, via the degenerate Riemann-Hilbert map, the WKB approximation of Stokes matrices recovers the Gelfand-Tsetlin integrable systems whose action variables match with period on spectral curves. If time permits, we will also briefly discuss the potential ramifications to cluster theory, spectral networks and gl(n)-crystals (in the quantum setting). The talk is based on joint work with Anton Alekseev and Xiaomeng Xu and ongoing discussions with Andrew Neitzke.

mathematical physicsalgebraic geometrydifferential geometrygeometric topologyoperator algebrasrepresentation theorysymplectic geometry

Audience: researchers in the topic

Geometry, Physics, and Representation Theory Seminar

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