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### Braid group actions in homotopy categories.

**Geometry/Topology**

Speaker: | Dr. Mikhail Khovanov, Mathematics, UC Davis |

Location: | 693 Kerr |

Start time: | Wed, Feb 16 2000, 4:10PM |

In this series of two talks I will construct a faithful braid group action in the homotopy category of complexes of modules over a certain finite-dimensional algebra (joint work with Paul Seidel). This action contains the braid group action on simple curves on a punctured disc and "descends" to the Burau representation. No prior knowledge of homotopy categories is necessary. Once noticed, these finite-dimensional algebras can be easily observed in many areas of algebra and geometry, and we will sketch their relationship with simple Lie algebras, modular representation theory of finite groups and the McKay correspondence (joint with Stella Huerfano).