Conformal Field Theory and Vertex Operator Algebras

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This course is an introduction to two-dimensional conformal field theory.

This is a well-developed branch of mathematical physics with many connections to

other topics in mathematics such as infinite-dimensional Lie algebras, vertex operator algebras,

modular tensor categories and theory of modular forms. The course aims at a thorough exposition

of the main structure that includes conformal geometry on the (extended) complex

plain, correlation functions, Ward identities, radial quantisation, operator product expansion, Virasoro algebra and conformal families.

The emphasis in the course is on the conceptual clarity rather than on the breadth of examples and

connections. It also aims at developing the basic computational skills in performing operator product expansions and those related to

Virasoro algebra representations. A detailed set of notes will be provided along with suggestions for complementary reading.