Conformal Field Theory and Vertex Operator Algebras

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Description

Monday 09.00-11.00

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. 

Assessment: two take home assignments are planned:

Assignment 1

Release Date: Monday 10 November (week 6)

Due Date: Monday 24 November (week 8).

Weighting: 40% of the final mark. 

Assignment 2

Release Date: to be made available by the end of week 10 

Due Date: Monday 21 January 2026.

Weighting:  60% of the final mark.