On the wall-crossing formula for quadratic differentials

Dylan G. L. Allegretti

doi:10.1093/imrn/rnac071

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arXiv · 2006.08059

On the wall-crossing formula for quadratic differentials

Dylan G. L. Allegretti

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Abstract

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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BibTeX RIS

Dylan G. L. Allegretti. 2020-06-15. On the wall-crossing formula for quadratic differentials. https://doi.org/10.1093/imrn%2Frnac071

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