### Lectures on Conformal Field Theory

**References:**

- G. Segal,
"Definition of Conformal Field Theory".
- K. Gawedzki,
"Lectures on Conformal Field Theory".
- E. Frenkel, D. Ben-Zvi,
"Vertex Algebras and Algebraic Curves".
- G. Moore, N. Seiberg,
"Lectures on RCFT".

**Part I: Geometry and Conformal Field Theory**

- Lecture I. Introduction. Toy-Model: 2d Topological Field Theory (pdf).
- Lecture II. Segal's axioms and constructive approach. Energy-momentum
tensor and its transformations (pdf).
- Lecture III. Ward identities and simplest OPEs (pdf).
- Lecture IV. Space of states and Virasoro Algebra
(pdf).
- Lecture V. Back to Segal's axioms. Path integral interpretation (pdf).

**Part II: Vertex operator algebras and applications**

- Lecture VI. Definition of Vertex Algebra (pdf).
- Lecture VII. Example: Heisenberg Vertex Algebra (pdf).
- Lecture VIII. Dong's Lemma. Reconstruction theorem. More examples of VOAs (pdf).
- Lecture IX. Associativity and Operator Product Expansion (pdf).
- Lecture X. Operator Product Expansion: applications. Correlation Functions(pdf).
- Lecture XI. Further examples. Lattice VOAs, boson-fermion correspondence (pdf).
- Lecture XII. Free fields, path integrals and vertex algebras
(pdf).

**Rational CFT**

- Lecture I. Correlation functions, conformal blocks and intertwining operators
(pdf).
- Lecture II. Properties of chiral vertex operators. Degenerate conformal
families (pdf).
- Lecture III: Minimal Models and Coulomb gas formalism
(pdf).
- Lecture IV. Conformal Field Theory and Quantum Groups
(pdf).

**Chiral de Rham complex and Mirror symmetry**

- Lecture I. Introductory notions. Chiral de Rham complex
(pdf).
- Lecture II. Line bundles, zeros of their sections and vertex algebras
(pdf).
- Lecture III. Logarithmic coordinates
(pdf).