Marston Conder: Regular and chiral maps with given valency or given type

The organizers of the Algebraic Graph Theory International Webinar would like to invite you to join us and other colleagues on February 16, 2021, at 7pm Central European Time, for the next presentation delivered by Marston Conder.

He will speak on Regular and chiral maps with given valency or given type

Abstract: A map is 2-cell embedding of a connected graph in a closed surface, breaking up the surface to simply-connected regions called faces. The map is called regular' if its automorphism group has a single orbit on flags (which are like incident vertex-edge-face triples), ororientably-regular' if the surface is orientable and the automorphism group of the map has a single orbit on arcs (incident vertex-edge pairs). If a map of the latter kind admits no reflections (e.g. fixing an arc but swapping the two faces incident with it), then the map is called chiral'. In such maps with a high degree of symmetry, all vertices have the same valency, say k, and all faces have the same size, say m, and then we call the ordered pair {m,k} thetype' of the map.

Writing a section of a forthcoming book on such maps (with Gareth Jones, Jozef Siran and Tom Tucker) has prompted me to review and extend what is known about regular and chiral maps with given valency k, or with given type {m,k}, including what happens in the special case where the automorphism group is isomorphic to an alternating or symmetric group. I will summarise findings in this talk.

Further details may be found at http://euler.doa.fmph.uniba.sk/AGTIW.html where you can also find the slides and the recordings of our previous presentations. Also, if you wish to advertise an AGT friendly conference on this page, please send us the link.

Hoping to see you at the webinar, and wishing you all the best. Stay AGTIW.

Isabel Hubard, Robert Jajcay and Primož Potočnik