# On transformations in the PainlevĂ© family

## Ronnie Nagloo

### CUNY Graduate Center

The PainlevĂ© equations are nonlinear 2nd order ODE and come in six families *P _{1}–P_{6}*, where

*P*consists of the single equation

_{1}*y′′=6y*, and

^{2}+t*P*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. 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 PainlevĂ© equations from the families

_{2}–P_{6}*P*.

_{1}–P_{6}Dr. Joel (Ronnie) Nagloo studies model theory and differential algebra. He holds a Ph.D. from Leeds University, completed under the supervision of Anand Pillay and Frank Nijhoff. After an initial postdoctoral position at the CUNY Graduate Center, he is now an Assistant Professor in mathematics at Bronx Community College.