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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
Moonshine and Connections
Monstrous Moonshine
The Monster Group
j-Invariant Expansions
McKay-Thompson Series
Moonshine Module V♮
Generalized Moonshine
Other Sporadic Groups
Umbral Moonshine
Mock Modular Forms
Quantum Moonshine
Geometric Connections
Chiral Algebras
D-Modules
Geometric Langlands
Factorization Algebras
Number Theory Applications
Modular Forms
L-Functions
Galois Representations
Arithmetic Geometry
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14. Rationality and Finiteness
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16. Computational Aspects