I am currently a research fellow in the School of Mathematics at the University of Bristol. I've previously been a visiting scholar at the University of Washington, a postdoctoral member of MSRI, and a member of the Institute for Advanced Study. Before all that, I was a graduate student at the University of Michigan, where I got my Ph.D. (in 2009) under the supervision of Jeffrey Lagarias. I work primarily in number theory, and I especially enjoy analytic number theory and experimentation.
- Computations of the Riemann zeta function. Source code here.
- Character sums
- The LMFDB
- Elliptic curves over Q(sqrt 5)
- (with Leo Goldmakher, Andrew Granville, and Dimitris Koukoulopoulos) The frequency and the structure of large character sums
- Averages of character sums
- (with Leo Goldmakher) Pólya-Vinogradov and the least quadratic nonresidue
- (with J. Brian Conrey, David W. Farmer, Akio Fujii, Sally Koutsoliotas, Stefan Lemurell, Michael Rubinstein, Hiroyuki Yoshida) The highest lowest zero of general L-functions. J. Number Theory 147 (2015), 364–373.
- (with Alyson Deines, Ariah Klages-Mundt, Benjamin LeVeque, R. Andrew Ohana, Ashwath Rabindranath, Paul Sharaba, and William Stein) A database of of elliptic curves over $\Q(\sqrt 5)$ - First report. in ANTS X: Proceedings of the Tenth Algorithmic Number Theory Symposium
- Conditionally bounding analytic ranks of elliptic curves. in ANTS X: Proceedings of the Tenth Algorithmic Number Theory Symposium
- (with Leo Goldmakher) The distribution of the maximum of character sums. Mathematika 59 (2013), no. 2, 427–442.
- (with Emanuel Carneiro, Kevin Hughes, and Lillian Pierce) On a discrete version of Tanaka's theorem for maximal functions. Proceedings of the AMS 140 (2012), no. 5
- (with Jason Bell) Bounded step functions and factorial ratio sequences. International Journal of Number Theory 5 (2009), no. 8, 1419--1431.
- Factorial ratios, hypergeometric series, and a family of step functions. Journal of the London Mathematical Society (2) 79 (2009), no. 2, 422--444.