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On the wall-crossing formula for quadratic differentials

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arxiv 2006.08059 v2 pith:7H7YLLE6 submitted 2020-06-15 math.GT hep-thmath.AGmath.CA

Dylan G. L. Allegretti This is my paper · ORCID
classification math.GThep-thmath.AGmath.CA
keywords formulawall-crossingappearingautomorphismsdifferentialquadraticalgebraicanalysis
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We prove an analytic version of the Kontsevich-Soibelman wall-crossing formula describing how the number of finite-length trajectories of a quadratic differential jumps as the differential is varied. We characterize certain birational automorphisms of an algebraic torus appearing in this wall-crossing formula using Fock-Goncharov coordinates. As an application, we compute the Stokes automorphisms for the Voros symbols appearing in the exact WKB analysis of Schr\"odinger's equation.

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