Two Lax systems for the Painleve II equation

Analysis Seminar
Thursday, April 2, 2015 - 11:05am for 1 hour (actually 50 minutes)
rm 005
Karl Liechty – DePaul University
Jeff Geronimo

Please Note: Karl Liechty is the winner of the 2015 Szego prize in orthogonal polynomials and special functions.

I will discuss two different Lax systems for the Painleve II equation. One is of size 2\times 2 and was first studied by Flaschka and Newell in 1980. The other is of size 4\times 4, and was introduced by Delvaux, Kuijlaars, and Zhang in 2010. Both of these objects appear in problems in random matrix theory and closely related fields. I will describe how they are related, and discuss the applications of this relation to random matrix theory.