# PEM

## Seminar

### Painleve systems arising from integrable hierarchies

Seminar Room 1, Newton Institute

#### Abstract

I will give an overview of a class of Lax representations for Painlev¥'e equations and their generalization in terms of Lie algebras. In that context discrete symmetries of Painlev¥'e systems are described by means of birational Weyl group actions. I will also discuss how they are related to integrable hierarchies associated with affine Lie algebras.