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.
Papers and Preprints:
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.
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.
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.
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.
Proportion of ordinarity in some families of curves over finite fields.
Arxiv page (2019).
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:
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.
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.