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We use generating functions to relate the expected values of polynomial factorization statistics over $mathbb{F}_q$ to the cohomology of ordered configurations in $mathbb{R}^3$ as a representation of the symmetric group. Our methods lead to a new proof of the twisted Grothendieck-Lefschetz formula for squarefree polynomial factorization statistics of Church, Ellenberg, and Farb.
A portrait is a combinatorial model for a discrete dynamical system on a finite set. We study the geometry of portrait moduli spaces, whose points correspond to equivalence classes of point configurations on the affine line for which there exist poly
We prove an estimate for spherical functions $phi_lambda(a)$ on $mathrm{SL}(3,mathbb{R})$, establishing uniform decay in the spectral parameter $lambda$ when the group parameter $a$ is restricted to a compact subset of the abelian subgroup $mathrm{A}
Let $M_{d,n}(q)$ denote the number of monic irreducible polynomials in $mathbb{F}_q[x_1, x_2, ldots , x_n]$ of degree $d$. We show that for a fixed degree $d$, the sequence $M_{d,n}(q)$ converges $q$-adically to an explicitly determined rational func
We give a recursive method for computing all values of a basis of Whittaker functions for unramified principal series invariant under an Iwahori or parahoric subgroup of a split reductive group $G$ over a nonarchimedean local field $F$. Structures in
In the following article we discuss Delaunay triangulations for a point cloud on an embedded surface in $mathbb{R}^3$. We give sufficient conditions on the point cloud to show that the diagonal switch algorithm finds an embedded Delaunay triangulation.