Research

I’m a PhD student of Jeff Hoffstein at Brown University. I research topics related to analytic number theory. My interests include $L$-functions, automorphic forms, metaplectic forms, Multiple Dirichlet Series, arithmetic geometry, and related topics.

On the side, I also enjoy looking into topics related to the mean value theorem of calculus. (Yes, really. It’s for fun, but it turns out that a lot of nice depth lurks behind some simple questions).

Current and Recent Papers

1. Traces, high powers and one level density for families of curves over finite fields, with Alina Bucur, Edgar Costa, Chantal David, and João Guerreiro, arXiv preprintSubmitted.
2. On Functions whose Mean-Value Abscissas are Midpoints,
with Paul Carter, arXiv preprint, paper announcementaccepted, to appear in American Mathematical Monthly.
3. Sign-Changes of Sums of Fourier Coefficients of Cusp Forms,
with Thomas Hulse, Chan Ieong Kuan, and Alexander Walker, arXiv preprint, paper announcementSubmitted.
4. Short-Interval Averages of Sums of Fourier Coefficients of Cusp Forms,
with Thomas Hulse, Chan Ieong Kuan, and Alexander Walker,
arXiv preprint,  paper announcement,  To appear in the Journal of Number Theory.
5. The Second Moment of Sums of Coefficients of Cusp Forms,
with Thomas Hulse, Chan Ieong Kuan, and Alexander Walker,
arXiv preprint, paper announcementTo appear in the Journal of Number Theory.
6. Taylor’s Theorem and a General Order Mean Value Theorem, Submitted.
7. Unexpected Conjectures about -5 modulo primes, Classroom Capsule
College Math Journal, Vol 46 No 1, January 2015.