Sarah Arpin

University of Colorado, Boulder

Office: Math 216
Email: Sarah DOT Arpin AT Colorado DOT edu

About Me

I am on the job market!

I am a New Yorker who moved to Colorado in August 2016 for graduate school. In Colorado, I enjoy math, dancing, and low-humidity weather.

I enjoy number theory especially, ever since taking an introductory level course as an undergraduate at Sarah Lawrence College. I am so glad that I had the opportunity to see how beautiful math is beyond Calculus, and I hope to help my students see this as well.

In Fall 2021, I began my sixth year as a PhD student at CU Boulder. I am studying number theory and arithmetic geometry with Dr. Katherine E. Stange.

I am a member of the CU Math Department Diversity Committee. I (re-)started the peer mentorship program for our department, and connected this program to the Diversity Committee.

I co-organize Front Range Number Theory Day, a bi-annual conference for number theorists in the front range region of the U.S.


Here it is

Research Interests

I enjoy applying arithmetic geometry tools to number theory problems motivated by post-quantum cryptography. I particularly like problems relating to supersingular elliptic curve isogeny graphs.


  • 10/9/2019: CU Boulder Mathematics Graduate Student Seminar. Introduction to Supersingular Elliptic Curve Isogeny Graphs. Slides
  • 10/26/2019: Number Theory Series LA, Occidental College. An Exploration of Supersingular Elliptic Curve Isogeny Graphs. Slides
  • 1/9/2021: Joint Mathematics Meeting. An Exploration of Supersingular Elliptic Curve Isogeny Graphs. Slides
  • 5/13/2021: UC Davis Number Theory Seminar. An Exploration of Supersingular Elliptic Curve Isogeny Graphs.
  • 10/14/2021: UC Irvine Number Theory Seminar. Adding Level Structure to Supersingular Elliptic Curve Isogeny Graphs.Slides
  • 10/21/2021: What is... A Seminar? What is… supersingular elliptic curve cryptography? Slides
  • 11/22/2021: Ohio State University Number Theory Seminar. Slides
  • 12/17/2021: West Coast Number Theory. Slides Lehmer Prize Recipient.
  • 01/2022: Joint Mathematics Meeting. BIKE Decoders and Error Detection. (Delayed)
  • 01/13/2022: Simons Collaboration on Arithmetic Geometry, Number Theory, and Computation Annual Meeting. Lightning Talk on Supersingular Elliptic Curve Isogeny Graphs with Level Structure.


  • Adventures in Supersingularland, with Catalina Camacho-Navarro, Kristin Lauter, Joelle Lim, Kristina Nelson, Travis Scholl, Jana Sotáková. To appear in Experimental Mathematics.
  • On the arithmetic of a family of superelliptic curves, with Richard Griffon, Libby Taylor, and Nicholas Triantafillou. Submitted.
  • The Scheme of Monogenic Generators and its Twists, with Sebastian Bozlee, Leo Herr, and Hanson Smith. Partially submitted.


    A place for me to put miscellaneous items that may or may not be of use to anyone else.

  • Interested in supersingular isogeny graph stuff, but not sure where to start? Here's a short(ish) (and thus incomplete) literature summary.
  • What primes p would be good for supersingular 2 or 3-isogeny graphs? Here are the calculations to get optimal graph conditions: Good Primes

    Spring 2022 Course Information

  • This semester, I am teaching Math 2300: Calculus 2, Section 006.

    MARCO/Office Hours:

  • MARCO hour: Monday 9pm - 10pm on Zoom
  • Office hour: TBD

    Previous Teaching at CU Boulder

  • Fall 2016: College Algebra TA
  • Spring 2017: Calculus 1 TA
  • Fall 2017: Math 1310 TA
  • Spring 2018: Math 1310 Instructor
  • Fall 2018: Math 1310 Instructor
  • Spring 2019: Math 2300 Instructor
  • Fall 2019: Math 2300 Instructor
  • Spring 2020: Math 2400 TA
  • Fall 2020: Math 1300 Instructor
  • Spring 2021: Math 2510 Instructor

    Sage Code

  • Sage Worksheet: Supersingular Isogeny Graph Diffie-Hellman Key Exchange

    Completed Analysis Prelim (Qual) Exams

    Completed Algebra Prelim (Qual) Exams

    Updated: 10/13/21