CFT+VOA

Schedule (Feel free to volunteer for any talks)

0. Oct 15: Organisation
1. Oct 22: Conformal transformation [S] Chapter 1 (Sridhar Hariharakrishnan) — Notes
2. Oct 29: Conformal group [S] Chapter 2 (Dang Dang) — Notes
3. Nov 5: Virasoro algebra [S] Chapter 5 (Karolis Dembickas) — Notes
4. Nov 12: Representation Theory of Virasoro algebra [S] Chapter 6 (Bangxin Wang) — Notes
5. Nov 19: Wightman axioms [S] Chapter 8.1–8.3 (Sridhar Hariharakrishnan) — Notes
6. Nov 26: Wightman axioms (cont) [S] Chapter 8.4–8.6 (Karolis Dembickas) — Notes
7. Dec 3: Wightman 2-D QFT with conformal symmetry [S] Chapter 8.7, 9.1–9.2 (Dang Dang) — Notes
8. Dec 10: Wightman 2-D QFT with conformal symmetry continued [S] Chapter 9.3–9.4 & [K] Chapter 1.1–1.2 (Dang Dang) — Notes
9. Dec 17: Definition of Vertex algebra and formal distributions [K] Chapter 1.3–1.4, 2.1–2.3 (Bangxin Wang) — Notes
10. Jan 7: More on locality and current, Virasoro algebra [K] Chapter 2.4–2.6 (Kostya Tolmachov) — Notes
11. Jan 14: Operator product expansion (OPE) & Wick’s theorem [K] Chapter 3.1–3.3 (Sridhar Hariharakrishnan) — Notes
12. Jan 21: Free boson/fermion vertex algebras [K] Chapter 3.5–3.6 (Karolis Dembickas) — Notes
13. Jan 28: “Reconstruction” theorem for vertex algebras [K] Chapter 4.1–4.6 (Dang Dang)

Basic notions in differential geometry, complex/functional analysis (Tangent space, Cauchy integral, Fourier series, ...).
First course in Lie group/algebra and representation (PBW basis, Verma modules, induced reps, triangular decomposition, ...).
Basics on cohomology and central extension of Lie algebras (Reviewed in [S] Chapters 3 and 4).
No physics background will be assumed, though it will be helpful.

Conformal Field Theory: Martin Schottenloher, A Mathematical Introduction into Conformal Field Theory, 2nd ed. [S]
Plauschinn & Blumenhagen, Introduction to Conformal Field Theory (applications to string theory)
Pavel Mnev, Lecture notes on Conformal Field Theory
Vertex Operator Algebra: Victor Kac, Vertex Algebras for Beginners [K]
Frenkel & Ben-Zvi, Vertex Algebras and Algebraic Curves
J. Lepowsky & H. Li, Introduction to Vertex Operator Algebras and Their Representations