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Sydney Mathematical Research Institute

Audience: Researchers in the topic
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SMRI-Double Header Seminar: ‘Stubborn conjectures concerning rewriting systems, geodesic normal forms and geodetic graphs’ Adam Piggott (Australian National University) & ‘Which groups have polynomial geodesic growth?’ Murray Elder (University of Technology Sydney)

Time & Date: Thursday 8 Apr 2021 1500-1700 Venue: Quad Oriental Room S204 (University of Sydney staff, students and affiliates only) & Online Via Zoom, register here: uni-sydney.zoom.us/meeting/register/tZMrdeyrqTkoGNIG0BAyuvcTjuBxA7MPDTvC

Talk 1: 3:00pm ’Stubborn conjectures concerning rewriting systems, geodesic normal forms and geodetic graphs’ Adam Piggott (Australian National University)

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).

Bio: Adam Piggott is a pure mathematician at the Australian National University. He is interested in combinatorial and geometric problems in groups, often groups arising as automorphisms of other groups. A recent interest is to continue the program started by computer scientists and mathematicians in the 1980s to classify the groups presented by various families of rewriting systems.

Talk 2: 4:00pm ’Which groups have polynomial geodesic growth?’ Murray Elder (University of Technology 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 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 Šuníc.

Bio: Murray is a pure mathematician at the University of Technology Sydney. He is interested in the complexity (time, space, language, combinatorial, other) of problems coming out of group theory (and other places). Recent work includes describing the set of all solutions to an equation over a free (or virtually free, or hyperbolic) group as a formal language of surprisingly low complexity, and giving an algorithm which constructs the finite description of the formal language in very low degree polynomial space.

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