Research Interests:

My research interest lies at the intersection of number theory and arithmetic geometry. On the one hand, on the number theory side, I work on local-global representation theory, automorphic forms, and classical modular forms ; on the other hand, I pursue various projects on elliptic curves over global and local fields on the arithmetic geometry side. Another part of my research focuses on exploring the connection between number theory and arithmetic geometry using L-functions and Galois representations, which broadly comes under the Langlands Program. Recently, I am also working on a few projects in computational number theory.

• On classical modular forms and automorphic forms.

See the articles 4, 5, 6, 7, 8, 11,10 listed below.


• On elliptic curves over number fields and local fields.

See the articles 2, 3 and 10 listed below.


• Connection between number theory and arithmetic geometry.

See the articles 9, 13, 15 below.

Publications and Preprints:

(The versions below might differ slightly from their published counterparts.)

1. Creating a dynamic database of finite groups (with Lewis Combes, John W. Jones, Jennifer Paulhus, David Roe, and Sam Schiavone).
   Preprint, 2024.


2. Supercongruences arising from Ramanujan-Sato Series(with Angelica Babei , Holly Swisher, Bella Tobin, and Fang-Ting Tu).
   Preprint, 2024 (Submitted).


3. Towards a classification of p^2-discriminant ideal twins over number fields(with Alyson Deines, Asimina S. Hamakiotes, Andreea Iorga, Changningphaabi Namoijam, and Lori D. Watson).
   Preprint, 2024, (Submitted).


4. Prime isogenous discriminant ideal twins(with Alexander J. Barrios, Alyson Deines, Maila Hallare, and Piper Harris).
   Preprint, 2024, (Submitted).


5. The quaternionic Maass Spezialschar on split SO(8) (with Jennifer Johnson-Leung, Finn McGlade, Isabella Negrini and Aaron Pollack).
   Preprint, 2024, (Submitted).


6. Classical and adelic Eisenstein series (with Ralf Schmidt and Shaoyun Yi).
   Preprint, 2024, (to appear in Rocky Mountain J. Math).


7. Generalized Ramanujan-Sato Series Arising from Modular Forms (with Angelica Babei , Lea Beneish , Holly Swisher, Bella Tobin, and Fang-Ting Tu).
   In: Bucur, A., Ho, W., Scheidler, R. (eds) Research Directions in Number Theory. Association for Women in Mathematics Series, vol 33. (2024), Springer, Cham, DOI.


8. Dimension formulas for Siegel modular forms of level 4 (with Ralf Schmidt and Shaoyun Yi, and with an appendix "Modular forms of Klingen level 4 and small weight" by Cris Poor and David Yuen), Mathematika 69 (2023), no. 3, 795-840, DOI.


9. The completed standard L-function of modular forms on G_2 (with Fatma Çiçek, Giuliana Davidoff, Sarah Dijols, Trajan Hammonds, and Aaron Pollack).
   Mathematische Zeitschrift 302 (2022), 483–517, DOI.


10. Representations attached to elliptic curves with a non-trivial odd torsion point (with Alexander J. Barrios).
    Bulletin of the London Mathematical Society, 2022, (published online), DOI.


11. Local data of rational elliptic curves with non-trivial torsion (with Alexander J. Barrios).
    Pacific Journal of Mathematics 318 (2022), No.1,1-42, DOI.


12. Congruences for dimensions of spaces of Siegel cusp forms and 4-core partitions (with Chiranjit Ray and Shaoyun Yi).
    The Ramanujan Journal 58 (2022), 1011-1023, DOI.


13. On counting cuspidal automorphic representations for GSp(4) (with Ralf Schmidt and Shaoyun Yi).
    Forum Mathematicum 33 (2021), no. 3, 821-843, DOI.


14. Paramodular forms coming from elliptic curves.
    Journal Number Theory 233 (2022), 126-157, DOI.


15. Elliptic curves and paramodular forms.
    Doctoral dissertation, University of Oklahoma, 2019.


16. Level of Siegel modular forms constructed via sym^3 lifting.
    Automorphic forms and related topics, Contemp. Math.,732 (2019), 225-227, DOI.