Research
TMy primary areas of interest are Arithmetic Geometry and Arithmetic Statistics. My thesis involves studying the p-divisible groups of Abelian Varieties and counting rational points on certain moduli stacks. I am generally interested in the theory of heights on various spaces. More recently, I have been interested in questions of rationality of varieties, derived categories of stacks and unlikely intersections in positive characteristic.
Papers and Preprints:
Frobenius distributions of low dimensional abelian varieties over finite fields
With Santiago Arango-Piñeros and Deewang Bhamidipati
Arxiv page (2023). To appear in IMRN.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.Derived equivalences of gerbey curves.
With Libby Taylor
Arxiv page (2020).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). Submitted.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.