Representations of configurations, maps and polytopes
The research will focus on structural properties, classification and enumeration of configurations, bf maps and polytopes relevant for their combinatorial and geometric representations, as well as on development of relevant algorithms. Relations between geometry and symmetries will be studied in various geometries, both for finite and infinite structures. We will also deal with regular and chiral abstract polytopes and their frequency of appearance through by studying infinite families of finite (almost simple) groups and their actions. We will investigate representing configurations via graphs and vice versa, construction and classification of new classes of (symmetric) configurations, highly incident configurations. Incidence geometries and strongly regular graphs will be studied as well.
Involved: Pisanski, Leemans, Conder, Berman, Schulte