Discrete Mathematics Seminar - Spectra of Farey Maps and Graphs

Speaker: Margaret Stanier (Open University)

Abstract: We determine the spectra of a class of cartographic maps called Farey maps, which are regular maps on oriented surfaces defined by congruence subgroups of the modular group. Our strategy is to find some general results for those maps which are regular coverings of other maps whose spectrum is known. Then we apply the same techniques to find the spectra of the underlying graphs of Hecke maps, which are defined, in the same way as Farey maps, by certain subgroups of Hecke groups.