What do we know about non-commutative Painlevé equations?

Announcing the first Research Seminar Quantum Fields and Strings of the semester, Wednesday October 15, at 13:30, at room 1.221 (CSMB building) Zum Großen Windkanal 2, 12489 Berlin.

Dr. Irina Bobrova, (MPI, Leipzig) will give a talk on “What do we know about non-commutative Painlevé equations?”; see abstract below.

Abstract:

The celebrated differential Painlevé equations define new special functions whose properties generalise those of elliptic functions. They provide certain classes of solutions of integrable PDEs, possess a Hamiltonian structure, and admit an isomonodromic representation, which gives rise to the so-called monodromy manifolds. In addition to these, one can obtain discrete analogues of the Painlevé equations, which are closely connected with affine Weyl groups and rational surfaces. It turns out that integrable PDEs have matrix, quantum, or, more generally, non-commutative analogues and can be reduced to the corresponding versions of the Painlevé equations. Thus, there is a natural question as to which properties of the latter can be extended to the non-commutative setting, and how. In this talk, I will present a summary of some results concerning this question.