Victor Kac (MIT) – Lecture I

http://www.crm.sns.it/course/4433/

Introduction to vertex algebras, Poisson vertex algebras, and integrable Hamiltonian PDE

Minicourse of the session “Vertex algebras, W-algebras, and applications”

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.