# Mathematics Colloquia and Seminars

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### Fusion of representations of affine Lie algebras and functorial conformal field theory

**Algebra & Discrete Mathematics**

Speaker: | James Tener, UCSB |

Related Webpage: | http://web.math.ucsb.edu/~jtener/research.html |

Location: | 2112 MSB |

Start time: | Mon, Nov 27 2017, 10:00AM |

Affine Lie algebras at positive integral level provide fundamental examples of 2d conformal field theories. A notion of `fusion product' of modules over these Lie algebras was originally introduced by physicists, and today there are several mathematical formalizations of this operation. The fusion product, however, is just one component of a much richer geometric structure introduced by Graeme Segal in the '80s to describe conformal field theories, but examples of Segal's axioms never appeared. In this talk I will motivate Segal's functorial framework for conformal field theory in the case of affine Lie algebras, and describe how to construct examples using operator algebras. This is based on joint work with Andre Henriques.

Note early time change (10am) and room change.