Alexander Smith's papers
Here's a list of my papers with arXiv links.
Selmer groups in twist families
I am most well known for my work on the distribution of Selmer groups in twist families and its applications to the CohenLenstraGerth heuristics and to Goldfeld's conjecture. This work was the subject of my dissertation at Harvard. The following two paper sequence is the complete form of this work.
The distribution of \ell^\infty Selmer groups in degree \ell twist families (2022), in preparation.
The distribution of fixed point Selmer groups in twist families (2022), in preparation.
These papers subsume the following two papers. The first of these had already subsumed the second.
2^\inftySelmer groups, 2^\inftyclass groups, and Goldfeld's conjecture (2017), unsubmitted.
Governing fields and statistics for 4Selmer groups and 8class groups (2016), unsubmitted.
I am organizing a learning seminar about this work that will start in September 2022. Details are here.
Other recent work
I wrote two papers on the CasselsTate pairing with Adam Morgan. This material is used in my work on the distribution of Selmer groups.
The CasselsTate pairing for finite Galois modules, with Adam Morgan (2022), submitted.
Field change for the CasselsTate pairing and applications to class groups, with Adam Morgan (2022), submitted.
Thanks to the HondaTate theorem, the next two papers are about very similar topics in spite of their dissimilar titles.
Abelian varieties of prescribed order over finite fields, with Raymond van Bommel, Edgar Costa, Wanlin Li, and Bjorn Poonen (2021), submitted.
Algebraic integers with conjugates in a prescribed distribution (2021), submitted.
Less recent work
The following paper was based on my undergraduate work at Princeton under ShouWu Zhang. It pushed me into arithmetic statistics.
The congruent numbers have positive natural density (2016), in preparation.
My undergraduate papers:
Ball Packings with Periodic Constraints, with Robert Connelly and Jeffrey Shen, published in Discrete & Computational Geometry, 52.4 (2014).
Irreducible Canonical Representations in Positive Characteristic, with Benjamin Gunby and Allen Yuan, published in Research in Number Theory, 1.3 (2015).

