Rubtsov V. Painlevé monodromy varieties and quantization, talk at The Workshop on Integrable Nonlinear Equations, 18-24 October 2015, Mikulov, Czech Republic (abstract)

Speaker: Vladimir Rubtsov

Title: Painlevé monodromy varieties and quantization

Abstract:
We discuss quantum algebras related to affine cubics arising as monodromy data varieties for confluented Painlevé equations.

We describe some examples of non-commutative cubics unifying the "quantum Painlevé cubics" and cubic superpotentials for 3D (generalized) Sklyanin algebras. Such general potentials appear in a description of moduli spaces of vacuum states in $N=4$ supersymmetric Yang-Mills field theory.