Research

My primary areas of interest are arithmetic geometry and arithmetic statistics, particularly in the context of rational points on varieties and stacks.  My research program broadly tries to understand how the arithmetic of such spaces is influenced by their geometry.  My thesis involved studying  invariants of p-divisible groups of abelian varieties and counting rational points on certain moduli stacks. More recently, I have been interested in questions of rationality of varieties over non-algebraically closed fields and in algebraic cycles on varieties over finite fields.

Upcoming Preprint: 

The integral Hasse principle for stacky curves associated to a family of generalized Fermat equations
With Juanita Duque Rosero, Chris Keyes, Andrew Kobin, Manami Roy and Yidi Wang.
Preprint available on request. 

Papers and Preprints:

• 1. Conic bundle threefolds differing by a constant Brauer class and connections to rationality
     With Sarah Frei, Lena Ji, Bianca Viray and Isabel Vogt
     Arxiv page (2024). Submitted.

  2. Frobenius distributions of low dimensional abelian varieties over finite fields
     With Santiago Arango-Piñeros and Deewang Bhamidipati
     International Mathematics Research Notices, Volume 2024, Issue 16, August 2024, Pages 11989–12020,
     Arxiv page (2023). Published version.

  3. Curve classes on conic bundle threefolds and applications to rationality
     With Sarah Frei, Lena Ji, Bianca Viray and Isabel Vogt
     Algebraic Geometry 11 (3) (2024) 421--459
     Arxiv page (2022). Published version.

  4. Counting elliptic curves with a rational N-isogeny.
     With Brandon Boggess
     Journal of Number Theory, (262)(September 2024) 471--505
     Arxiv page (2020). Published version.

  5.  Proportion of ordinarity in some families of curves over finite fields.
     Arxiv page (2019).

  6. On integers that are uniquely representable by modified arithmetic progressions.
     With Sartak Chimni and Amitabha Tripathi,
     Notes on Number Theory and Discrete Mathematics 22, no. 3 (2016): 36--44.

Expository Articles:

1. On rational points on classifying stacks and Malle's conjecture
   With Shabnam Akhtari, Jennifer Park and Marta Pieropan
   Arxiv page (2024). To appear in Proceedings of WIN5. 

2. Heights over finitely generated fields.
   With Stephen McKean
   In:  Stacks Project Expository Collection (London Mathematical Society Lecture Note Series, Cambridge University Press). Editors: Belmans, P., Ho, W., \& De Jong, A. (Eds.). (2022).
   Preprint.