School of Mathematics & Physics, University of Lincoln
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.