Factorization statistics and the twisted Grothendieck-Lefschetz formula

Abstract

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 ${\mathbb{R}}^2$.

Extended abstract for arXiv:1802.00305. To appear in Proceedings of 30th Conference on Formal Power Series and Algebraic Combinatorics (2018)

References in corpus (1)

• Polynomial splitting measures and cohomology of the pure braid group