This paper goes beyond Katz–Sarnak theory on the distribution of curves over finite fields
according to their number of rational points, theoretically, experimentally, and conjecturally …

We prove geometric and cohomological stabilization results for the universal smooth degree
d hypersurface section of a fixed smooth projective variety as d goes to infinity. We show that …

Let B (g, p) denote the number of isomorphism classes of g-dimensional Abelian varieties
over the finite field of size p. Let A (g, p) denote the number of isomorphism classes of …

There is a natural probability measure on the set of isomorphism classes of principally
polarized Abelian varieties of dimension $ g $ over $\mathbb {F} _q $, weighted by the …

The moduli stack of principally polarized abelian surfaces comes equipped with the
universal abelian surface. The fiber of π over a point corresponding to an abelian surface A …

The present thesis provides a survey of results and techniques from the Langlands program
which allow for the computation of the ℓ-adic cohomology of local systems on Shimura …

Arithmetic statistics is the study of number-theoretic objects in aggregates, rather than in
isolation. This study takes many different forms, but in this paper we will concentrate on …

The similarity between the density of the primes and the density of irreducible polynomials
defined over a finite field of q elements was first observed by Gauss. Since then, many other …

We analyze the variation around the mean of the distribution of the number of rational points
on non-hyperelliptic genus 3 curves over finite fields, by extrapolating from results on the …

Abstract Poonen's Closed Point Sieve has proven to be a powerful technique for producing
structural and combinatorial results for varieties over finite fields. In this thesis we will …