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### Hydra Groups

**Algebra & Discrete Mathematics**

Speaker: | Tim Riley, Cornell |

Location: | 1147 MSB |

Start time: | Fri, Jan 22 2010, 1:10PM |

I will describe some wild geometry that arises in an apparently benign group theoretic setting: I will exhibit a family of groups enjoying a number of restrictive geometric and algebraic conditions (they are CAT(0), bi-automatic, 1-relator, and free-by-cyclic), and yet these groups have free subgroups of huge (Ackermannian) distortion. The origin of this behaviour lies in a simple computational game --- a realisation of Hercules' battle with the hydra, played out in manipulations of strings of letters. This is work with Will Dison.