## Heidi Goodson

## Assistant Professor

## Brooklyn College

I'm an Assistant Professor of Mathematics at Brooklyn College. I graduated from the University of Minnesota with a PhD in Mathematics in May 2016.

In Spring 2019, I am teaching Abstract Algebra 1 and Calculus 2. Course syllabi (last updated January 22):

My courses and interactions with students are built up from the following axioms written by Professor Federico Ardila at San Francisco State University:

- Axiom 1. Mathematical talent is distributed equally among different groups, irrespective of geographic, demographic, and economic boundaries.
- Axiom 2. Everyone can have joyful, meaningful, and empowering mathematical experiences.
- Axiom 3. Mathematics is a powerful, malleable tool that can be shaped and used differently by various communities to serve their needs.
- Axiom 4. Every student deserves to be treated with dignity and respect.

My research lies in the field of number theory. I investigate arithmetic properties of curves and higher dimensional varieties over finite fields. In my thesis work, I used hypergeometric functions to give point count formulas for families of algebraic varieties over finite fields and to study the relationship between certain period integrals and the trace of Frobenius of these varieties. More recently, I have been interested in studying how the number of **F**p-points on a particular curve or family of curves varies as the prime p goes to infinity. This area of number theory is commonly known as the study of Sato-Tate distributions.

If you are a student interested in research and learning more about number theory, please send me an email!

For more info on the math I like to teach and do, see my CV (last updated: February 2019).

When I'm not doing math, I'm usually riding a bike. I race with a small group of fast and smart women on Mathletes Racing. For more info on the bikes I like to ride and race, please stop by my office and ask me!

**Journal Articles:**

- "An Identity for Vertically Aligned Entries in Pascal's Triangle," January 2019. Submitted. Preprint.
- "Towards the Sato-Tate Groups of Trinomial Hyperelliptic Curves," (with M. Emory and A. Peyrot). November 2018. Submitted. Preprint.
- "Hypergeometric Properties of Genus 3 Generalized Legendre Curves," Journal of Number Theory. May 2018. Preprint.
- "A Complete Hypergeometric Point Count Formula for Dwork Hypersurfaces," Journal of Number Theory. October 2017. Preprint.
- "Hypergeometric Functions and Relations to Dwork Hypersurfaces," International Journal of Number Theory. March 2017. Preprint.
- "Effective Congruences for Mock Theta Functions," (with N. Andersen, H. Friedlander, and J. Fuller), Mathematics. 2013; 1(3):100-110. Preprint

**Math Travel in 2018/2019:**

- September: Conference on Open Questions in Cryptography and Number Theory in Irvine, California.
- October: 2018 Québec-Maine Number Theory Conference in Quebec, Canada.
- March: Hofstra University Mathematics Seminar
- June: Travel is supported by an AWM-NSF Travel Grant .
- Number-Theoretic Methods in Cryptology in Paris, France.