# Ben Knudsen: Extremal stability for configuration spaces

**Time: **
Thu 2022-05-12 11.15 - 12.15

**Location: **
Kräftriket, House 6, Room 306

**Participating: **
Ben Knudsen (Northeastern University)

**Abstract:**

We study the longterm behavior of the rational Betti numbers of configuration spaces of manifolds, regarded as functions of the number of particles. According to classical homological stability, the Betti number in fixed dimension is eventually equal to a polynomial in the number of particles, whose degree is bounded in terms of the dimension 0 homology of the manifold. We prove a dual result, namely that the Betti number in fixed codimension is eventually equal to a quasi-polynomial in the number of particles, whose degree is bounded in terms of the codimension 1 homology of the manifold. This talk represents joint work with Jeremy Miller and Philip Tosteson.