Research

During fall 2020, I am a Postdoctoral Fellow at the CRM thematic semester “Cohomology in Arithmetic”. In the 2019-2020 academic year, I was a Postdoctoral Scholar at Vanderbilt University, where my mentor was Larry Rolen. 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, including but not restricted to classical and Hilbert modular forms, quaternionic orders and orders in central simple algebras, and Bruhat-Tits buildings. I use a variety of computer algebra systems, and I primarily code in Magma and Sage.

I am involved in a collaborative project for implementing a new environment for Hilbert modular forms in Magma.

Publications

1. Type numbers of orders in central simple algebras. In preparation.

2. The Riemann Hypothesis for period polynomials of Hilbert modular forms (with Larry Rolen and Ian Wagner). Journal of Number Theory. 10.1016/j.jnt.2020.07.004, 2020. (preprint)

3. Metacommutation of primes in Eichler orders (with Sara Chari). Acta Arithmetica. 10.4064/aa191031-23-5, 2020. (preprint)

4. 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.