On some structures of the second Painlevé equation and related hierarchies

Abstract: This talk is divided into two parts. The first part is general: we will discuss what the Painlevé equations are and what structures they have, namely integrability, confluences, Hamiltonian structures, sigma-coordinates and symmetries. In the second part, we will consider some integrable hierarchies associated with the second Painlevé equation, their sigma-coordinates, symmetries, and further generalizations to non-commutative cases.

arxiv.org/abs/2010.10617, arxiv.org/abs/2012.11010

mathematical physicsalgebraic geometrydifferential geometrydynamical systemssymplectic geometry

Audience: researchers in the topic

( paper )

Junior Global Poisson Workshop II