# Daniele Valeri

## Integrability of classical affine W-algebras

Classical affine W-algebras $W(\mathfrak g,O)$ are algebraic structures associated to a simple Lie algebra $\mathfrak g$ and a nilpotent orbit $O$. In this talk we will describe how to associate to $W(\mathfrak g,O)$ an integrable hierarchy of PDEs. When $O$ is the principal nilpotent orbit one gets the Drinfeld–Sokolov hierarchy, which gives the famous Korteweg–de Vries hierarchy for $\mathfrak g=sl_2$.

The talk is based on joint works with Alberto De Sole, Mamuka Jibladze and Victor G. Kac.