Mateja Šajna (University of Ottawa)
Cycle Systems: A Neverending Fascination

This talk begins with an account of the fascinating history of combinatorial designs and cycle systems. We then introduce some of the most important problems involving cycle systems: cycle decomposition of complete (and nearly complete) graphs, and the Oberwolfach problem, both in its directed and undirected variant. We briefly sketch some of the proofs of the solved problems, and give an update on the status of the open ones. Finally, we discuss the author‘s progress (joint work with Andrea Burgess and Patrick Niesink) on the directed Oberwolfach problem with constant cycle lengths.