SMRI Seminar Double-Header, 8 April: Adam Piggott & Murray Elder – Geodesics in Groups

SMRI Seminar Double-Header
Piggott ‘Stubborn conjectures concerning rewriting systems, geodesic normal forms and geodetic graphs’ & Elder ‘Which groups have polynomial geodesic growth?’
Adam Piggott  (Australian National University)
Thursday, 8 April 2021, 15:00–16:00 AEST (Sydney)
Location: Online via Zoom

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).

Murray Elder  (University of Technology Sydney)
Thursday, 8 April 2021, 16:00–17:00 AEST (Sydney)

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, and by myself, Alex Bishop, Martin Brisdon, José Burillo and Zoran Šunić.

Please register to attend.
The seminar will be held online via Zoom. You will be sent a confirmation email with connection details.

This seminar will be recorded and made available on the SMRI Youtube channel.