Research

During Fall 2021- Summer 2023, I was a postdoctoral fellow at McMaster University, working with Cameron Franc. I have also been a postdoctoral researcher at Dartmouth College as part of the Simons Collaboration on Arithmetic Geometry, Number Theory, and Computation, a postdoctoral fellow at the CRM thematic semester “Cohomology in Arithmetic”, and a Postdoctoral Scholar at Vanderbilt University. I got my Ph.D. from Dartmouth College in 2019, under the supervision of Thomas R. Shemanske.

My research interests lie broadly in algebraic number theory from a computational aspect. Specifically, I study orders in semisimple algebras, their arithmetic subgroups, and modular forms. I use a variety of computer algebra systems, and I primarily code in Magma and Sage.

Publications

1. Zeta functions for table algebras and fusion rings with irrational-valued characters (with Allen Herman). Submitted for publication. (arXiv)

2. A database of basic numerical invariants of Hilbert modular surfaces (with Eran Assaf, Benjamin Breen, Edgar Costa, Juanita Duque-Rosero, Aleksander Horawa, Jean Kieffer, Avinash Kulkarni, Grant Molnar, Sam Schiavone, and John Voight). To appear in LMFDB, Computation, and Number Theory (LuCaNT). (arXiv)

3. Generalized Ramanujan-Sato series arising from modular forms (with Lea Beneish, Manami Roy, Holly Swisher, Bella Tobin, and Fang-Ting Tu). To appear in Research Directions in Number Theory: Women in Numbers V. (arXiv)

4. Families of \(\phi \)-congruence subgroups of the modular group (with Andrew Fiori and Cameron Franc). Mathematika, 69: 1104-1144, 2023. (PDF)

5. Computing zeta functions of table algebra orders using the Bushnell-Reiner integral approach. (with Allen Herman). Mediterr. J. Math. 20, 108 (2023). (arXiv)

6. Type numbers of orders in central simple algebras. Preprint (arXiv)

7. The Riemann Hypothesis for period polynomials of Hilbert modular forms (with Larry Rolen and Ian Wagner). Journal of Number Theory, 218 (2021), 44-61. (arXiv)

8. Metacommutation of primes in Eichler orders (with Sara Chari). Acta Arithmetica, 197:1 (2021), 77-92. (arXiv)

9. Computing normalizers of tiled orders in \(M_n(k) \), Proceedings of the Thirteenth Algorithmic Number Theory Symposium, edited by Renate Scheidler and Jonathan Sorenson, Open Book Series 2, Mathematical Sciences Publishers, Berkeley, 2019, 55-68. (PDF)

You can also read my Ph.D. thesis here. A caveat: example 2.3.6. is wrong, but it does not affect the results in the thesis.