# Blog Archives

# Topic Archive: Painleve equations

Model theory seminarKolchin seminar in Differential AlgebraFriday, September 19, 201412:30 pmGC 5382

# Model theory and the PainlevĂ© equations

CUNY Graduate Center

The PainlevĂ© equations are nonlinear 2nd order ODEs 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.