Alison Beth Miller

Alison 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, particularly algebraic number theory. I currently work in arithmetic invariant theory and arithmetic statistics, and have explored connections with 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.

Publications and preprints

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, online publication in International Mathematics Research Notices. (arxiv preprint)

PhD Thesis: Counting Simple Knots via Arithmetic Invariants.

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


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 postdoc at Rice University.

Alison L. Miller is a developmental psychologist at the University of Michigan.