# Algebra seminar in Lincoln: talk by Prof. Colva Roney-Dougal

On the 20th of November 2019, **Prof. Colva Roney-Dougal (University of St Andrews)** visited Charlotte Scott Centre for Algebra and gave a talk “Polynomial-time proofs that groups are hyperbolic”.

*Abstract*: A finitely-presented group *G* is hyperbolic if there is a linear bound on the number of relators required to prove that a word of length *n* is equal to the identity in *G*. The word problem in a group that is known to be hyperbolic is solvable in linear time. However, it is undecidable in general whether a group is, in fact, hyperbolic. This talk will present some efficient, low-degree polynomial-time procedures which seek to prove that a given finitely-presented group is hyperbolic. If successful, they can also often construct, in low-degree polynomial time, a linear time word problem solver and a quadratic time conjugacy problem solver. This is joint work with Derek Holt, Steve Linton, Max Neunhoffer, Richard Parker and Markus Pfeiffer.

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