| Speaker: Isabelle Steinmann Affiliation: University of Auckland Time: 15:00 Thursday, 19 August, 2021 Location: 303-257 |
| A Cayley graph is constructed from a generating set for a group and gives a diagrammatic representation of that group. Planar groups (groups which have a Cayley graph embeddable in the sphere) were classified by Maschke in 1896. An interesting question, to which no answer has been published, is whether there exists a finite non-planar group which has a Cayley graph that embeds in the projective plane. I will give an outline of the proof that the only two such groups are C3xC3 and C3xS3 and show in greater detail that there are no 5-valent Cayley graphs of non-planar groups embeddable in the projective plane. The proof involves aspects of algebra, combinatorics and topology and the development of new methods that could be helpful in answering other questions about graph embeddings. |