## 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.

### My CV

Here it is
### Research Interests

I am particularly interested in supersingular elliptic curve isogeny graphs.

### Talks

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)
### Papers

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.
### Blurbs

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

I worked on these exams with Andy Riddle over winter break 2016, with the invaluable help of Cliff Blakestad. (Fewer graduate students stick around for winter break.)
If you also helped but are not listed above, I apologize! I probably just forgot. Please send me an email to remind me.

- August 2007
- August 2009
- August 2010
- January 2010
- August 2012
- January 2013
- August 2014
- August 2015
- August 2016
I welcome feedback! These solutions are certainly incomplete and may contain errors. If/when you find an error, please send me an email about it.

Updated: 3/21/21