# Daniele Valeri (Yau Mathematical Sciences Center)

## Classical affine W-algebras for $$gl_N$$ and associated integrable hierarchies

I will describe a new method of integrability for Hamiltonian hierarchies of PDEs based on the notion of an Adler type pseudodifferential operator and the theory of quasideterminants. I will then show how to use this method to construct an integrable hierarchy associated to every classical affine W-algebra for $$gl_N$$. Joint work with A. De Sole and V. Kac.