**CARMA COLLOQUIUM***Maths Honours Student Presentation***Location:**Room V206, Mathematics Building (Callaghan Campus) The University of Newcastle**Time and Date:**3:00 pm, Thu, 25^{th}Nov 2010**Speaker:**Mr Chris Banks, CARMA, The University of Newcastle**Title:***Locally primitive groups acting on regular trees***Speaker:**Mr James Mainey, School of Mathematical and Physical Sciences, The University of Newcastle**Title:***TBA***Speaker:**Mr Chris Maitland, School of Mathematical and Physical Sciences, The University of Newcastle**Title:***Methods for packing complete graphs with cycles***[Permanent link]**
Automorphism groups of locally finite trees form a significant class of examples of locally compact totally disconnected topological groups. In this talk I will discuss my honours research, which covered the various local properties of automorphism groups. I will provide methods of constructing such groups, in particular groups acting on regular trees, and discuss what conclusions we can make regarding the structure of these groups. This talk will be an introduction to cycle decompositions of complete graphs in the context of Alspach's conjecture about the necessary and sufficient conditions for their existence. Several useful methods of construction based on algebra, graph products and modifying existing decompositions will be presented. The most up to date results on this problem will be mentioned and future directions of study may be suggested. |