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

- 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 preprint,
*Submitted.* - On Functions whose Mean-Value Abscissas are Midpoints,

with Paul Carter, arXiv preprint, paper announcement,*accepted, to appear in***American Mathematical Monthly***.* - Sign-Changes of Sums of Fourier Coefficients of Cusp Forms,

with Thomas Hulse, Chan Ieong Kuan, and Alexander Walker, arXiv preprint, paper announcement,*Submitted.* - 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**. -
The Second Moment of Sums of 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***.* - Taylor’s Theorem and a General Order Mean Value Theorem,
*Submitted.* - Unexpected Conjectures about -5 modulo primes,
*Classroom Capsule*,

**College Math Journal,**Vol 46 No 1, January 2015.