abstract: Preliminary Course Outline:
(1) Introduction to vertex algebras, the extension theorem. (2) Introduction to Poisson vertex algebras and Lenard-Magri scheme of integrability of Hamiltonian equations. (3) Variational de Rham complex (4) Classical Hamiltonian reduction and classical W-algebras (5) Non-local Poisson vertex algebras and Dirac reduction (6) Double Poisson (vertex) algebras and non-commutative Hamiltonian equations.