Symmetries of Discrete Structures in Geometry (17w5015)
The Casa Matemática Oaxaca (CMO) will host the "Symmetries of Discrete Structures in Geometry" workshop from August 20th to August 25th, 2017. Symmetry is among the most frequently recurring themes in mathematics and the sciences. The 5-day Workshop will focus on geometric, combinatorial and algebraic aspects of highly-symmetric discrete structures such as polytopes, polyhedra, maps, incidence geometries, and hypertopes. In each case the presence of high symmetry ensures a powerful interplay between geometric intuition and algebraic structure. Recent years have seen an outburst of research activities focussing on discrete symmetric objects. A major goal of the Workshop is to capitalise on this momentum and gather experts and emerging researchers from diverse areas of geometry and combinatorics to discuss recent developments (over the last 5-10 years) on discrete symmetric structures, encourage new collaborations, and achieve progress on pressing open questions in the field. Key open problems include: topological classification of abstract chiral polytopes; developing a theory of hypertopes, as hybrids of polytopes and incidence geometries; polytope-theoretic interpretation for sporadic simple groups; group-theoretical classifications of regular and chiral polytopes; and classification of highly symmetric skeletal polyhedral structures in ordinary space.
