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### Word processing in the mapping class group of a surface

**Geometry/Topology**

Speaker: | Howard Masur, University of Illinois at Chicago and UC Berkeley |

Location: | 693 Kerr |

Start time: | Tue, May 2 2000, 2:30PM |

This talk represents joint work with Yair Minsky. The ultimate goal is to apply the theory of hyperbolic spaces and groups to study algorithmic questions in the mapping class group. The starting point is the theorem that the complex of curves is a delta hyperbolic space. This result is hard to apply directly since the complex is locally infinite. To overcome this obstacle we introduce a combinatorial mechanism which describes sequences of elementary moves in the graph of markings. These tools are applied to give a family of quasigeodesics in the mapping class group and a linear bound on the shortest word conjugating two pseudo-Anosov elements.