Research

My 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:

• 1. Frobenius distributions of low dimensional abelian varieties over finite fields
     With Santiago Arango-Piñeros and Deewang Bhamidipati
     Arxiv page (2023)

  2. Curve classes on conic bundle threefolds and applications to rationality
     With Sarah Frei, Lena Ji, Bianca Viray and Isabel Vogt
     Arxiv page (2022). To appear in Algebraic Geometry.

  3. Derived equivalences of gerbey curves.
     With Libby Taylor
     Arxiv page (2020).

  4. Counting elliptic curves with a rational N-isogeny.
     With Brandon Boggess,
     Arxiv page (2020).

  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. 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.