Vertex Algebras

  1. Mathematical Preliminaries
    1. Formal Power Series Theory
      1. Single Variable Formal Series
        1. Basic Definitions
          1. Algebraic Operations
            1. Convergence Considerations
              1. Ring Structure
              2. Multivariable Formal Series
                1. Symmetric Functions
                  1. Antisymmetric Functions
                    1. Mixed Symmetry Types
                      1. Manipulation Rules
                    2. Formal Distribution Theory
                      1. The Formal Delta Function
                        1. Definition and Basic Properties
                          1. Sifting Property
                            1. Delta Function Identities
                              1. Derivatives of Delta Functions
                              2. General Formal Distributions
                                1. Linear Operations
                                  1. Product Operations
                                    1. Composition Rules
                                  2. Rational Function Expansions
                                    1. Laurent Series Expansions
                                      1. Partial Fraction Decomposition
                                        1. Residue Calculations
                                          1. Taylor Formula Applications
                                          2. Combinatorial Aspects
                                            1. Binomial Theorem Extensions
                                              1. Generating Functions
                                                1. Symmetric Function Theory

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                                              1. Foundations and Motivation

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                                              3. Basic Structure of Vertex Algebras