Georgia Institute of Technology College of Sciences

Over the past 40 years, researchers have made many connections between the dimension of posets and the issue of planarity for graphs and diagrams, but there appears to be little work connecting dimension to structural graph theory. This situation has changed dramatically in the last several months. At the Robin Thomas birthday conference, Gwenael Joret, made the following striking conjecture, which has now been turned into a theorem: The dimension of a poset is bounded in terms of its height and the tree-width of its cover graph. In this talk, I will outline how Joret was led to this conjecture by the string of results on planarity. I will also sketch how the resolution of his conjecture points to a number of new problems, which should interest researchers in both communities.