Groups Acting on Trees Without Involutive Inversions

The concept of symmetry, which is formalised using the algebraic notion of groups, is an ever-present field of interest within the mathematical community. We can investigate such
symmetry groups and their actions on mathematical objects to further our understanding of how different symmetries work, and to characterise new and interesting symmetry groups. In this project, we consider such symmetry group actions on d-regular trees, which act like one of finitely many prescribed ‘local actions’ with the aim of identifying new congruency classes of group actions on said graphs. We propose to accomplish this by building upon the work done by Burger-Mozes while restricting the local action of such groups to edge neighbourhoods rather than vertex neighbourhoods, thereby gaining a new perspective on these graph symmetries within the context of the Weiss Conjecture.

Jack Berry

The University of Newcastle

Jack Berry is a student at the Newcastle of University studying Physics and Mathematics. His interests lie on the border between pure mathematics and theoretical physics. While completing his bachelor of science, Jack has developed a broad range of skills from pure mathematics to more experimental physics, working on multiple research projects with the Priority Research Centre for Organic Electronics (COE) where he spent time developing and modelling organic photovoltaic devices with applications for solar cells. As he is approaching the end of his bachelor degree, Jack looks forward to the next stage in his academic career where he will commence his Honours research year in the area of quantum information theory.

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