Algebra Seminar: Dancso -- A mystery of matching expansions

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.