Sarah Arpin

University of Colorado, Boulder

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

About Me

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 all levels of math, and I am available as a tutor for middle school, high school and undergraduate math students who are not in Math 1300 (send me an email!).

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 2020, I began my fifth year as a PhD student at CU Boulder. I am studying number theory and arithmetic geometry with Dr. Katherine E. Stange.


Here it is

Research Interests

I am particularly interested in 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 (TBD)


  • 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.


    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 2021 Course Information

  • This semester I am an instructor for Math 2510 (Stats) section 006. See our Canvas page for details.

    MARCO/Office Hours:

  • MARCO: Monday 10am - 11am, 2pm - 3pm
  • Open Office Hour (in the usual classroom Zoom): Wednesday 9:30am - 10:30am
  • Section 6 Only Office Hour: Wednesday 10:30am - 11:30am

    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

    Sage Code

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

    Completed Analysis Prelim (Qual) Exams

    Completed Algebra Prelim (Qual) Exams

    Updated: 3/21/21