Seminar

The Painlevé equations are nonlinear 2nd order ODE and come in six families P1 - P6, where P1 consists of the single equation y'' = 6y^2 + t, and P2 - P6 come with some complex parameters. They were discovered strictly for mathematical considerations at the beginning of the 20th century but have arisen in a variety of important physical applications including for example random matrix theory and general relativity. In this talk I will explain how one can use model theory to answer the question of whether there exist algebraic relations between solutions of different Painlevé equations from the families P1 - P6.