Heidi Goodson, PhD

I'm an arithmetic geometer working on projects related to Sato-Tate distributions and the geometry of Shimura varieties.

My research has been supported by funding from the National Science Foundation (DMS - 2201085), The Professional Staff Congress and The City University of New York, and 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 and the recipient of the 2026 Tow Award for Excellence Mentoring.

You can find some slides from recent talks here: Talks

Making progress at AIM in 2025

Published Research Articles:

"Degeneracy and Sato-Tate groups of y^2=x^{p^2}−1," (with J. Chen, R. Hoque, and S. Malikah). to appear in Arithmetic Geometry, Number Theory, and Computation, Contemporary Mathematics. preprint
- Code available here: https://github.com/justinyc1/Degeneracy-and-Sato-Tate-Groups-of-C_p2
"Monodromy groups and exceptional Hodge classes, I: Fermat Jacobians," (with A. Gallese and D. Lombardo). to appear in The Indiana University Mathematics Journal. Preprint.
- Code available here: https://github.com/G4ll/The-monodromy-field-of-Fermat-Jacobians
"Nondegeneracy and Sato-Tate Distributions of Two Families of Jacobian Varieties," (with M. Emory). Research in Number Theory (2026). Open Access link.
"On invariants of Artin-Schreier curves," (with J. Duque-Rosero, E. Lorenzo García, B. Malmskog, R. Scheidler). Research Directions in Number Theory - Women in Numbers 6 (2026). Open Access link
"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). Documenta Mathematica (2026). Preprint.
"Sato-Tate Groups and Distributions of y^ℓ=x(x^ℓ−1)," (with R. Hoque). Acta Arithmetica (2025). Preprint and Online First version.
- 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/
"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
"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 (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 link.
"An Identity for Vertically Aligned Entries in Pascal's Triangle," Notes on Number Theory and Discrete Mathematics. July, 2020. Open Access link.
- 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

Preprints:

"On the classification of indecomposable Ekedahl-Oort strata in unitary Shimura varieties, and related Newton polygons," (with E. Andrews, D. Bhamidipati, M. Fox, S. Groen, S. Nair). 2026. Preprint.
"The Ekedahl-Oort and Newton stratification of the 𝖦𝖴(3,2) Shimura variety," (with E. Andrews, D. Bhamidipati, M. Fox, S. Groen, S. Nair). 2025. preprint
"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.
"Ekedahl-Oort strata in the GU(q-2,2) Shimura variety," (with E. Andrews, D. Bhamidipati, M. Fox, S. Groen, S. Nair). 2024. 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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