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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
17.
Applications and Related Areas
17.1.
Conformal Field Theory
17.1.1.
Physical Interpretations
17.1.2.
Correlation Functions
17.1.3.
Partition Functions
17.1.4.
Boundary Conditions
17.2.
String Theory Applications
17.2.1.
Heterotic Strings
17.2.2.
Compactification
17.2.3.
Mirror Symmetry
17.2.4.
Topological Strings
17.3.
Integrable Systems
17.3.1.
KdV Hierarchies
17.3.2.
Tau Functions
17.3.3.
Soliton Theory
17.3.4.
Quantum Groups
17.4.
Algebraic Geometry
17.4.1.
Moduli Spaces
17.4.2.
Sheaf Theory
17.4.3.
Derived Categories
17.4.4.
Mirror Symmetry
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16. Computational Aspects
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1. Foundations and Motivation