CARMA SEMINAR Speaker: Assoc Prof Murray Elder, CARMA, The University of Newcastle Title: A Metropolis Markov Chain algorithm to sample trivial words and compute cogrowth in finitely generated groups; or -- F is not amenable. Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 4:00 pm, Thu, 21st Nov 2013 Abstract: In this talk I will describe an algorithm to do a random walk in the space of all words equal to the identity in a finitely presented group. We prove that the algorithm samples from a well defined distribution, and using the distribution we can find the expected value for the mean length of a trivial word. We then use this information to estimate the cogrowth of the group. We ran the algorithm on several examples -- where the cogrowth series in known exactly our results are in agreement with the exact results. Running the algorithm on Thompson's group $F$, we see behaviour consistent with the hypothesis that $F$ is not amenable. [Permanent link]