Different approaches for constructing non-abelian Painlevé equations

Abstract: The famous Painlevé equations play a significant role in modern mathematical physics. The interest in their non-commutative extensions was motivated by the needs of modern quantum physics as well as by natural attempts of mathematicians to extend ‘’classical’’ structures to the non-commutative case.

In this talk we will consider several approaches that are useful for detecting non-commutative analogs of the Painlevé equations. Namely, the matrix Painlevé-Kovalevskaya test, integrable non-abelian auxiliary autonomous systems, and infinite non-commutative Toda equations. All of these methods allow us to find a finite list of non-abelian candidates for such analogs. To provide their integrability, one can present an isomonodromic Lax pair.

This talk is based on a series of papers joint with Vladimir Sokolov and on arXiv:2205.05107 joint with Vladimir Retakh, Vladimir Rubtsov, and Georgy Sharygin (publ. in J. Phys. A: Math. Theor.).

mathematical physicsdynamical systemsquantum algebrarepresentation theorysymplectic geometry

Audience: general audience

( video )

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BIMSA Integrable Systems Seminar

Series comments: The aim is to bring together experts in integrable systems and related areas of theoretical and mathematical physics and mathematics. There will be research presentations and overview talks.

Audience: Graduate students and researchers interested in integrable systems and related mathematical structures, such as symplectic and Poisson geometry and representation theory.

The zoom link will be distributed by mail, so please join the mailing list if you are interested in attending the seminar.

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