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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
15.
Moonshine and Connections
15.1.
Monstrous Moonshine
15.1.1.
The Monster Group
15.1.2.
j-Invariant Expansions
15.1.3.
McKay-Thompson Series
15.1.4.
Moonshine Module V♮
15.2.
Generalized Moonshine
15.2.1.
Other Sporadic Groups
15.2.2.
Umbral Moonshine
15.2.3.
Mock Modular Forms
15.2.4.
Quantum Moonshine
15.3.
Geometric Connections
15.3.1.
Chiral Algebras
15.3.2.
D-Modules
15.3.3.
Geometric Langlands
15.3.4.
Factorization Algebras
15.4.
Number Theory Applications
15.4.1.
Modular Forms
15.4.2.
L-Functions
15.4.3.
Galois Representations
15.4.4.
Arithmetic Geometry
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14. Rationality and Finiteness
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16. Computational Aspects