 SYMMETRY IN NEWCASTLE
 Location: Room V109, Mathematics Building (Callaghan Campus) The University of Newcastle
 Dates: 12:00 pm, Fri, 2^{nd} Aug 2019  4:30 pm, Fri, 2^{nd} Aug 2019

Schedule:
121: Brian Alspach
12: Lunch
23: John Bamberg
33.30: Tea
3.304.30: Marston Conder
 Speaker: Prof. Brian Alspach, CARMA, The University of Newcastle
 Title: Honeycomb Toroidal Graphs
The honeycomb toroidal graphs are a family of graphs I have been looking at now and then for thirty years. I shall discuss an ongoing project dealing with hamiltonicity as well as some of their properties which have recently interested the computer architecture community.
 Speaker: A/Prof John Bamberg, University of Western Australia
 Title: Symmetric finite generalised polygons
Finite generalised polygons are the rank 2 irreducible spherical buildings, and include projective planes and the generalised quadrangles, hexagons, and octagons. Since the early work of Ostrom and Wagner on the automorphism groups of finite projective planes, there has been great interest in what the automorphism groups of generalised polygons can be, and in particular, whether it is possible to classify generalised polygons with a prescribed symmetry condition. For example, the finite Moufang polygons are the 'classical' examples by a theorem of Fong and Seitz (19731974) (and the infinite examples were classified in the work of Tits and Weiss (2002)). In this talk, we give an overview of some recent results on the study of symmetric finite generalised polygons, and in particular, on the work of the speaker with Cai Heng Li and Eric Swartz.
 Speaker: Prof. Marston Conder, Department of Mathematics, The University of Auckland
 Title: Edgetransitive graphs and maps
In this talk I'll describe some recent discoveries about edgetransitive graphs and edgetransitive maps. These are objects that have received relatively little attention compared with their vertextransitive and arctransitive siblings.
First I will explain a new approach (taken in joint work with Gabriel Verret) to finding all edgetransitive graphs of small order, using single and double actions of transitive permutation groups. This has resulted in the determination of all edgetransitive graphs of order up to 47 (the best possible just now, because the transitive groups of degree 48 are not known), and bipartite edgetransitive graphs of order up to 63. It also led us to the answer to a 1967 question by Folkman about the valencytoorder ratio for regular graphs that are edge but not vertextransitive.
Then I'll describe some recent work on edgetransitive maps, helped along by workshops at Oaxaca and Banff in 2017. I'll explain how such maps fall into 14 natural classes (two of which are the classes of regular and chiral maps), and how graphs in each class may be constructed and analysed. This will include the answers to some 18yearold questions by Širáň,
Tucker and Watkins about the existence of particular kinds of such maps on orientable and nonorientable surfaces.
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