Heidi Goodson, PhD

I'm a number theorist! In particular, I investigate the arithmetic and geometry of curves and abelian varieties over finite fields.

My research is supported by grants from the National Science Foundation (DMS - 2201085) and The Professional Staff Congress and The City University of New York. In Spring 2024 and 2025, my research with undergraduates was supported by the Brooklyn College Tow Mentoring and Research Program. I was the recipient of the 2022 - 2023 Brooklyn College School of Natural and Behavioral Sciences Research Award in Mathematics.

You can find some slides from recent talks here: Talks

Making progress at AIM in 2025

Research Articles:

"Traverso's Isogeny Conjecture for Some Unitary p-Divisible Groups," (with E. Andrews, D. Bhamidipati, M. Fox, S. Groen, S. Nair). 2025. preprint
"Monodromy groups and exceptional Hodge classes, II: Sato-Tate groups," (with A. Gallese and D. Lombardo). 2025. Preprint.
"Monodromy groups and exceptional Hodge classes, I: Fermat Jacobians," (with A. Gallese and D. Lombardo). 2024. Preprint.
- Code available here: https://github.com/G4ll/The-monodromy-field-of-Fermat-Jacobians
"Sato-Tate Groups and Distributions of y^ℓ=x(x^ℓ−1)," (with R. Hoque). Accepted to Acta Arithmetica. Preprint.
- Code available here: https://github.com/rezrezrezrez/ST-Groups-Distributions-of-C_ell.
- Our research was featured in the Brooklyn College Brief newsletter: https://www.brooklyn.edu/bc-brief/tow-mentoring-initiative-math-team-authors-peer-review-paper/
"Ekedahl-Oort strata and the supersingular locus in the GU(q-2,2) Shimura variety," (with E. Andrews, D. Bhamidipati, M. Fox, S. Groen, S. Nair). 2024. Preprint.
"On invariants of Artin-Schreier curves," (with J. Duque-Rosero, E. Lorenzo García, B. Malmskog, R. Scheidler). To appear in Research Directons in Number Theory - Women in Numbers 6. Preprint.
"Nondegeneracy and Sato-Tate Distributions of Two Families of Jacobian Varieties," (with M. Emory). 2024. Preprint.
"An Exploration of Degeneracy in Abelian Varieties of Fermat Type." Experimental Mathematics. June 2024. Preprint.
- Code available here: https://github.com/heidigoodson/Degeneracy_abvar_FermatType
"Mod l gamma factors and a converse theorem for finite general linear groups," (with J. Bakeberg, M. Gerbelli-Gauthier, A. Iyengar, G. Moss, R. Zhang). Accepted to Documenta Mathematica. Preprint.
"Sato-Tate Distributions of Catalan Curves," Journal de Théorie des Nombres de Bordeaux, Volume 35 (2023), pages 87–113. Preprint.
"Sato-Tate Distributions of y^2=x^p-1 and y^2=x^{2p}-1," (with M. Emory). Journal of Algebra, Volume 597 (May 2022), pages 241 - 265. Preprint.
"Towards the Sato-Tate Groups of Trinomial Hyperelliptic Curves," (with M. Emory and A. Peyrot). International Journal of Number Theory, Volume No. 17, Issue No. 10, pp. 2175 - 2206, Year 2021. Preprint.
"Examining the Modeling Framework of Crime Hotspot Models in Predictive Policing," (with A. Hoyer-Leitzel). Journal of Humanistic Mathematics. July 2021. Open-Access article.
"An Identity for Vertically Aligned Entries in Pascal's Triangle," Notes on Number Theory and Discrete Mathematics. July, 2020. Open-access article.
- This work is referenced on the Online Encyclopedia of Integer Sequences (Sequence A034807).
"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

Other Writing:

"Preparing for a Tenure-Track Job at an Urban Public College," (with D. Hubbard). Notices of the American Mathematical Society. August 2022, Volume 69, Number 7. Open-access article.
"A Few Firsts in the Epsilon Years of My Career," Journal of Humanistic Mathematics. July 2019. Open-access article

Thesis:

"Hypergeometric Functions and Arithmetic Properties of Algebraic Varieties," Ph.D. Thesis, University of Minnesota, 2016. pdf

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