On a classification of non-Abelian Painlevé equations

The famous Painlevé equations define the most general special functions and appear ubiquitously in integrable models. Since the latter have been intensively studied in the matrix or, more general, non-Abelian case, examples of non-Abelian Painlevé equations arise.
We will discuss the problem of classifying such equations. This talk is based on a series of papers joint with Vladimir Sokolov and an ongoing project with Vladimir Retakh, Vladimir Rubtsov, and Georgy Sharygin.