Symmetry Breaking in Discrete Structures (18w5050)


(Grenfell Campus, Memorial University)

Debra Boutin (Hamilton College)

Wilfried Imrich (Montanuniversität Leoben)

Thomas Tucker (Colgate University)


The Casa Matemática Oaxaca (CMO) will host the "Symmetry Breaking in Discrete Structures" workshop from September 16th to September 21st, 2018.

Can the vertices of a cube be can be colored using the colors black and white so that no symmetry of the cube preserves the coloring? The answer is no; three colors are required. On the other hand, four are needed for the tetrahedron and only two for the dodecahedron. In general, one can ask how many colors are needed to break the symmetry of any mathematical structure.

The idea of symmetry-breaking with colors first arose for networks, or “graphs”, in the 1970s, was rediscovered in 1996, and has generated more than 100 papers since then. But the notion of the “group” of all symmetries of a structure has been studied since the 19th century, and symmetry-breaking with colors also appeared in group theory papers of the 1980s. Moreover, the idea has been applied to many structures other than graphs. The goal of this workshop is to bring together graph theorists and group theorists to study symmetry-breaking in all its variations and contexts.

The Casa Matemática Oaxaca (CMO) in Mexico, and the Banff International Research Station for Mathematical Innovation and Discovery (BIRS) in Banff, are collaborative Canada-US-Mexico ventures that provide an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station in Banff is supported by Canada's Natural Science and Engineering Research Council (NSERC), the U.S. National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnología (CONACYT). The research station in Oaxaca is funded by CONACYT.