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SMRI Seminar Double-Header: Piggott ‘Stubborn conjectures concerning rewriting systems, geodesic normal forms and geodetic graphs’ & Elder 'Which groups have polynomial geodesic growth?'
Talk 1: 3:00pm
‘Stubborn conjectures concerning rewriting systems, geodesic normal forms and geodetic graphs’
Adam Piggott (ANU)

Abstract: A program of research, started in the 1980s, seeks to classify the groups that can be presented by various classes of length-reducing rewriting systems. We discuss the resolution of one part of the program (joint work with Andy Eisenberg (Temple University), and recent related work with Murray Elder (UTS).

Talk 2: 4:00pm
‘Which groups have polynomial geodesic growth?’
Murray Elder (UTS)

Abstract: The growth function of a finitely generated group is a powerful and well-studied invariant. Gromov's celebrated theorem states that a group has a polynomial growth function if and only if the group is 'virtually nilpotent'. Of interest is a variant called the 'geodesic growth function' which counts the number of minimal-length words in a group with respect to some finite generating set. I will explain progress made towards an analogue of Gromov's theorem in this case. I will start by defining all of the terms used in this abstract (finitely generated group; growth function; virtual property of a group; nilpotent) and then give some details of the recent progress made. The talk is based on the papers arxiv.org/abs/1009.5051, arxiv.org/abs/1908.07294 and arxiv.org/abs/2007.06834 by myself, Alex Bishop, Martin Brisdon, José Burillo and Zoran Šunić.


These seminars will be recorded and uploaded to https://www.youtube.com/c/SydneyMathematicalResearchInstituteSMRI

Apr 8, 2021 03:00 PM in Canberra, Melbourne, Sydney

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