Zsuzsanna Dancso (University of Sydney) Friday 15 November, 12-1pm, Place: Carslaw 375 Title: A mystery of matching expansions Abstract: There is a mysterious correspondence - in several steps, weaving through Lie theory - between invariants called "expansions" for two different classes of "topological objects": tangled tubes in R^4 and homotopy curves in a punctured disk. Half of the correspondence is due to Dror Bar-Natan and myself, the other half due to Alekseev, Kawazumi, Kuno and Naef. It is reasonable to believe that the only way to describe the relationship between these topological creatures cannot be a convoluted path through algebra, but must have a topological manifestation, eg, a map described in topological terms. I have searched for this map for some years now, with a long list of collaborators including our very own Hazel Browne. The bad news is, I have not found it. The good news is, I have gained an understanding of why the question is hard, and why the pre-requisites may be interesting in their own right.