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Mathematics
Vertex Algebras
1. Foundations and Motivation
2. Mathematical Preliminaries
3. Basic Structure of Vertex Algebras
4. Axioms and Fundamental Properties
5. Core Operations and Concepts
6. Fundamental Examples
7. Affine Vertex Algebras
8. Virasoro and Conformal Structure
9. Module Theory and Representations
10. Advanced Constructions
11. Intertwining Operators and Fusion
12. Zhu's Theory
13. Vertex Operator Superalgebras
14. Rationality and Finiteness
15. Moonshine and Connections
16. Computational Aspects
17. Applications and Related Areas
16.
Computational Aspects
16.1.
Structure Constants
16.1.1.
OPE Coefficient Calculations
16.1.2.
Fusion Rule Computations
16.1.3.
Character Calculations
16.1.4.
Modular Data
16.2.
Computer Algebra Methods
16.2.1.
Symbolic Computation
16.2.2.
Normal Form Algorithms
16.2.3.
Gröbner Basis Methods
16.2.4.
Representation Software
16.3.
Classification Problems
16.3.1.
Small Central Charge
16.3.2.
Minimal Models
16.3.3.
Exceptional Cases
16.3.4.
Systematic Approaches
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15. Moonshine and Connections
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17. Applications and Related Areas