Roubtsov V. Classical and quantum algebraic structures within Painlevé transcendents, talk at The Workshop on Geometry of PDEs and Integrability, 14-18 October 2013, Teplice nad Becvou, Czech Republic (abstract)

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Speaker: Vladimir Roubtsov

Title: Classical and quantum algebraic structures within Painlevé transcendents

Abstract:
There surprisingly many interesting algebraic structures related to all six Painlevé equations. The origin of it encodes in rich algebraic and Poisson geometry of affine cubics describing the monodromy data of these equations.

We shall review some of this structures, including elliptic Sklyanin algebras, non-commutative deformationss of quiver's potentials, related Calabi-Yau algebras and toric structures associated to character varieties together with their mutations. My talk is based on a joint paper with M. Mazzocco and a work in progress.

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