Factorization statistics and the twisted Grothendieck-Lefschetz formula

We announce recent results on a connection between factorization statistics of polynomials over a finite field and the structure of the cohomology of configurations in ${\mathbb{R}}^3$ as a representation of the symmetric group. This connection parallels a result of Church, Ellenberg, and Farb relating factorization statistics of squarefree polynomials and the cohomology of configurations in ${\mathbb{R}}^2$.