2025/05/06 by Tom Bridgeland, Bridgeland, Tom, Fabrizio Del Monte +1 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Mathematical and Theoretical Analysis #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.2505.03429
openalex publication_date 2025/05/06 · openalex created_date 2025/10/16 · openalex updated_date 2026/07/28
Joyce structures are a class of geometric structures that first arose in relation to Donaldson-Thomas theory. There is a special class of examples, called class S[A1], whose underlying manifold parameterises Riemann surfaces of some fixed genus equipped with a meromorphic quadratic differential with poles of fixed orders. We study two Joyce structures of this type using the isomonodromic systems associated to the Painlevé II and III3 equations. We give explicit formulae for the Plebański functions of these Joyce structures, and compute several associated objects, including their tau functions, which we explicitly relate to the corresponding Painlevé tau functions. We show that the behaviour of the Joyce structure near the zero-section can be studied analytically through poles of Painlevé equations. The systematic treatment gives a blueprint for the study of more general Joyce structures associated to meromorphic quadratic differentials on the Riemann sphere.