SMRI Seminar 8th April 2021

The Symmetry in Newcastle Seminar is not back just yet, but that does not mean you have to miss out on your monthly fix of Australian group theory seminars! Our friends at Sydney Mathematical Research Institute (SMRI) are hosting a seminar this Thursday and if you like combinatorial and geometric group theory, this might be just the event for you because the speakers for the day are Adam Piggott, Australian National University, and Murray Elder, University of Technology Sydney. The times, titles and abstracts of the talks, along with important links are as follows.

When: 8 April 2021, 15:00-17:00 AEST (05:00 – 07:00 UTC)

Where: Quad Oriental Room S204 (University of Sydney staff, students and affiliates only) and via Zoom (registration link below)

Talk 1: 15:00 AEST (05:00 UTC)

‘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: 16:00 AEST (06:00 UTC)
‘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 {\em virtually nilpotent}. Of interest is a variant called the {\em 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.

To Register: