Publications

1. Central values of zeta functions of non-Galois cubic fields
   with A. Södergren and N. Templier. Published in Inventiones Mathematicae (2026).
2. Geometry of numbers methods in the cusp with applications to class groups
   with A. Siad, A. A. Swaminathan, and I. Varma. Published in Algebra & Number Theory 19 (2025).
3. Squarefree values of polynomial discriminants II
   with M. Bhargava and X. Wang. Published in Forum of Mathematics, Pi (2025).
4. Counting integral points on symmetric varieties with applications to arithmetic statistics
   with A. Siad and A. A. Swaminathan. Published in Proceedings of the London Mathematical Society (2025).
5. Secondary terms in the first moment of |Sel₂(E)|
   with T. Taniguchi. Published in Cambridge Journal of Mathematics (2025).
6. The mean number of 2-torsion elements in the class groups of n-monogenized cubic fields
   with M. Bhargava and J. Hanke. Accepted in American Journal of Mathematics.
7. Malle's Conjecture for Galois octic fields over ℚ
   with I. Varma. Accepted in Journal für die reine und angewandte Mathematik (Crelle).
8. Asymptotics for the number of cubic fields ordered by general invariants
   with F. Thorne. Published in Commentarii Mathematici Helvetici (2024).
9. An improvement on Schmidt's bound on the number of number fields of bounded discriminant and small degree
   with M. Bhargava and X. Wang. Published in Forum of Mathematics, Sigma (2022).
10. Squarefree values of polynomial discriminants I
    with M. Bhargava and X. Wang. Published in Inventiones Mathematicae (2022).
11. Heuristics for the asymptotics of the number of S_n-number fields
    with J. Tsimerman. Published in Journal of the London Mathematical Society (2022).
12. Exceptional jumps of Picard ranks of reductions of K3 surfaces over number fields
    with A. N. Shankar, Y. Tang, and S. Tayou. Published in Forum of Mathematics, Pi (2021).
13. Large families of elliptic curves ordered by conductor
    with A. N. Shankar and X. Wang. Published in Compositio Mathematica (2020).
14. Bounds on 2-torsion in class groups of number fields and integral points on elliptic curves
    with M. Bhargava, T. Taniguchi, F. Thorne, J. Tsimerman, and Y. Zhao. Published in Journal of the American Mathematical Society (2020).
15. The number of quartic D4-fields ordered by conductor
    with A. Altug, K. Wilson, and I. Varma. Published in Journal of the European Mathematical Society (2019).
16. Odd degree number fields with odd class number
    with W. Ho and I. Varma. Published in Duke Mathematical Journal (2018).
17. Rational points on hyperelliptic curves having a marked non-Weierstrass point
    with X. Wang. Published in Compositio Mathematica (2018).
18. Sato-Tate equidistribution of certain families of Artin L-functions
    with A. Södergren and N. Templier. Published in Forum of Mathematics, Sigma (2017).
19. Binary quartic forms having bounded invariants, and the boundedness of the average rank of elliptic curves
    with M. Bhargava. Published in Annals of Mathematics (2015).
20. Ternary cubic forms having bounded invariants, and the existence of a positive proportion of elliptic curves having rank 0
    with M. Bhargava. Published in Annals of Mathematics (2015).
21. Counting S₅ fields with a power saving error term
    with J. Tsimerman. Published in Forum of Mathematics, Sigma (2014).
22. Abelian surfaces over finite fields with prescribed groups
    with C. David, D. Garton, Z. Scherr, E. Smith, L. Thompson. Published in Bulletin of the London Mathematical Society (2014).
23. On the Davenport-Heilbronn theorems and second order terms
    with M. Bhargava and J. Tsimerman. Published in Inventiones Mathematicae (2013).
24. The average rank of elliptic curves over number fields
    Ph.D. thesis, Princeton University (2013).

Preprints

1. Counting number fields of fixed degree by their smallest defining polynomial
   with S. Arango-Piñeros, F. Gundlach, R. J. Lemke Oliver, K. J. McGown, W. Sawin, A. Serrano López, and I. Varma. Posted to the arXiv (2026).
2. The existence of infinitely many cubic fields with class group of exact 2-rank 1
   with M. Bhargava, A. Siad, and A. A. Swaminathan. Posted to the arXiv (2026).
3. Secondary terms in the counting functions of quartic fields II
   with J. Tsimerman. Posted to the arXiv (2025).
4. The second moment of the size of the 2-class group of monogenized cubic fields
   with M. Bhargava and A. A. Swaminathan. Posted to the arXiv (2025).
5. Finiteness theorems for some representations of GL₃
   with F. Janbazi. Posted to the arXiv (2025).
6. Secondary terms in the counting functions of quartic fields I
   with J. Tsimerman. Posted to the arXiv (2025).
7. Nontrivial bounds on 2-, 3-, 4-, and 5-torsion in class groups of number fields, conditional on standard L-function conjectures
   with J. Tsimerman. Posted to the arXiv (2021).
8. The second moment of the 2-Selmer groups of elliptic curves
   with M. Bhargava and A. A. Swaminathan. Posted to the arXiv (2021).
9. Geometry of numbers methods over global fields I: Prehomogeneous vector spaces
   with M. Bhargava and X. Wang. Posted to the arXiv (2015).
10. The average size of the 5-Selmer group of elliptic curves is 6, and the average rank is less than 1
    with M. Bhargava. Posted to the arXiv (2013).
11. The average number of elements in the 4-Selmer groups of elliptic curves is 7
    with M. Bhargava. Posted to the arXiv (2013).
12. Geometry of numbers methods over global fields II: Coregular vector spaces
    with M. Bhargava and X. Wang. Preprint available on request.

Current courses

• MAT 202H5
• MAT 344H5