Louis Hainaut: Asymptotic growth in the homology of configuration spaces on graphs

Abstract: In this talk, I will discuss the homology of configuration spaces on graphs, and in particular present some results about how these homology groups grow as the number of points in the configuration increases. In the more classical setting of configuration spaces on a manifold, the existence of homological stability and representation stability, resp. for unordered and ordered configuration spaces, provides a tight control over the asymptotic growth in any given degree. By contrast, when working over a graph we don't have these stability phenomena since the homology groups grow too quickly for these stability phenomena to be present.

I will first introduce configuration spaces on graphs and explain how one can visualize some easy homology classes, and then present asymptotic growth results and some of the proof ideas. This is based on joint work with Ben Knudsen and Nick Wawrykow.