## University of Sydney Algebra Seminar

# Tim Riley (Cornell University)

## Friday 19th February, 11.05-11.55am, Carslaw 173 (note unusual time and venue)

### Hydra Groups

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.