# Mathematics Colloquia and Seminars

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### Nielsen--Thurston classification via the curve graph

**Geometry/Topology**

Speaker: | Mark Bell, University of Illinois at Urbana-Champaign |

Related Webpage: | http://math.illinois.edu/~mcbell/ |

Location: | 2112 MSB |

Start time: | Wed, Nov 2 2016, 3:10PM |

We will discuss a new polynomial-time algorithm, joint with Richard Webb, for computing the Nielsen--Thurston type of a mapping class. The procedure works by considering the maps action on the curve graph, which records the pairs of essential closed curves that are disjoint.

To be able to compute this action, we need to be able to construct geodesics through the curve graph. However, this graph is locally infinite and so standard pathfinding algorithms struggle. We will discuss a new refinement of the techniques of Leasure, Shackleton, Watanabe and Webb for overcoming this local infiniteness that allows such geodesics to be found in polynomial time (in terms of their length).