Geometry Seminar

I will discuss recent work with An and Drummond-Cole showing that the homology of configuration spaces of graphs exhibits eventual polynomial growth, an analogue of classical homological and representation stability results for manifolds. We compute the degree of this polynomial in terms of an elementary connectivity invariant, in particular verifying an upper bound conjectured by Ramos. Along the way, we uncover a new "edge stabilization" mechanism and a family of spectral sequences arising from a small chain model first introduced by Swiatkowski. Speaker(s): Ben Knudsen (Harvard)