Victor Kac, Lecture I – 9 December 2014

Victor Kac (MIT) – Lecture I

Introduction to vertex algebras, Poisson vertex algebras, and integrable Hamiltonian PDE
Minicourse of the session “Vertex algebras, W-algebras, and applications”

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.