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

TL;DR

This paper introduces vertex algebras, Poisson vertex algebras, and their applications to integrable Hamiltonian PDEs, providing foundational knowledge and insights into their mathematical structures and relationships.

Contribution

It offers an accessible introduction to the theory of vertex and Poisson vertex algebras and explores their relevance to integrable Hamiltonian partial differential equations.

Findings

Establishes foundational concepts of vertex algebras and Poisson vertex algebras.

Connects algebraic structures to integrable Hamiltonian PDEs.

Provides a comprehensive overview suitable for researchers in Lie theory and mathematical physics.

Abstract

These lectures were given in Session 1: "Vertex algebras, W-algebras, and applications" of INdAM Intensive research period "Perspectives in Lie Theory" at the Centro di Ricerca Matematica Ennio De Giorgi, Pisa, Italy, December 9, 2014 -- February 28, 2015.