Speaker: G. Sharygin

Date and time: 22.06.2022, 17:00 (GMT +03:00)

Title: Noncommutative Painleve 4 equation

Abstract: Let $R$ be a unital division ring, equipped with a differentiation $D$; if $t\in R$ verifies the equation $Dt=1$, we can regard $D$ as the operator $\frac{d}{dt}$. We develop a theory of Painleve 4 equation in $R$ with $t$ playing the role of time variable. It turns out that the classical results like B\"acklund transformations, Hamiltonian and symmetric forms of this equation, Hankel determinant formulas for the solutions etc. have noncommutative analogs in this case; in particular, one has to use Gelfand and Retakh theory of quasi-determinants instead of the usual Hankel determinants and deal with different types of Painleve 4 equation, depending on the formulas we choose. The talk is based on a joint work with I. Bobrova, V. Retakh and V. Rubtsov.

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