# Alison Beth Miller

**E-mail:**

abm (at) ams (dot) org

alimil (at) umich (dot) edu
I am a mathematician and an Associate Editor at Mathematical Reviews.

I am interested in number theory, broadly speaking, especially when there is interesting algebraic or geometric structure involved. I currently work primarily in arithmetic invariant theory, arithmetic statistics, and arithmetic dynamics. I have an ongoing interest in exploring connections with topology and knot theory, specifically related to the Alexander module and Blanchfield pairing.

I completed my PhD at Princeton in 2014 under Manjul Bhargava. From 2014-2019 I was an NSF and Benjamin Peirce postdoctoral fellow at Harvard University. Here is my CV (last updated June 2024).

## Publications and preprints

** Seifert surfaces in the four-ball and composition of binary quadratic forms**, with Menny Aka, Peter Feller, and Andreas Wieser (arxiv preprint)
**
Dynamical Mahler Measure: A survey and some recent results**, with Annie Carter, Matilde Lalín, and Michelle Manes (arxiv preprint), Proceedings of WIN5 (Women in Numbers 5), to appear

**
Two-variable polynomials with dynamical Mahler measure zero**, with Annie Carter, Matilde Lalín, Michelle Manes, and Lucia Mocz, *Research in Number Theory* 8, 25 (2022) (arxiv preprint).

**On the number of binary quadratic forms having discriminant 1−4p, p prime**, with Stanley Yao Xiao (arxiv preprint)

**Asymptotics for the number of Simple (4a+1)-Knots of Genus 1**, *International Mathematics Research Notices* Volume 2022, Issue 9, May 2022, Pages 6742–6769. (arxiv preprint)

PhD Thesis: Counting Simple Knots via Arithmetic Invariants.

See here for my older papers, mostly dating from my undergraduate years.

## Slides

Arithmetic statistics for knot invariants: PDF slides from my talk at the Boston University/Keio University 2019 Workshop on Number Theory.

## Old course websites and notes

Notes may contain typos: please contact me with any questions or corrections.

Math 223a: Local Class Field Theory notes (pdf), 2018 website, 2017 website

Math 223b: Global Class Field Theory notes (pdf), 2019 website, 2018 website

Math 221: Graduate Algebra notes (pdf)

Math 222: Lie Groups and Lie Algebras notes (pdf)

### People who might be confused with me

Allison N. Miller is a low-dimensional topologist and professor at Swarthmore College.
Alison L. Miller is a developmental psychologist at the University of Michigan.