Jajcay, Robert; Matematični kolokvij maj 2010

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Orientably regular Cayley maps

Robert Jajcay

Indiana State University, ZDA

20. maj 2010

Cayley maps are highly symmetric embeddings of Cayley graphs in orientable surfaces, and orientably regular Cayley maps are Cayley maps of the highest symmetry level possible. Even though Cayley maps have been officially discovered only at the end of the 20-th century, prior to them being named and defined, they already played an important role in several areas of mathematics and have connections to Riemann surfaces and elliptic functions, representations of groups and Galois groups.

In our talk, following a review of the history and motivation for the study of Cayley maps, we focus on the interplay of their algebraic, topological, and combinatorial properties. We report on the progress of several classification projects, and conclude with a recently discovered connection to the constructions of small regular graphs of large girth.

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