  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 $\mathbb{R}^2$.

Number Theory