$ \newcommand{\C}{\mathbb{C}} \newcommand{\R}{\mathbb{R}} \newcommand{\N}{\mathbb{N}} \newcommand{\Q}{\mathbb{Q}} \newcommand{\Z}{\mathbb{Z}} \newcommand{\wM}{\widetilde{M}} \newcommand{\Var}{\textrm{Var}} $

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.



  1. (with Sandro Bettin, Andrew R. Booker, Brian Conrey, Min Lee, Giuseppe Molteni, Thomas Oliver, David J. Platt, Raphael S. Steiner) A conjectural extension of Hecke's converse theorem
  2. (with Ghaith Hiary) New computations of the Riemann zeta function on the critical line
  3. (with Leo Goldmakher, Andrew Granville, and Dimitris Koukoulopoulos) The frequency and the structure of large character sums
  4. Averages of character sums
  5. (with Leo Goldmakher) Pólya-Vinogradov and the least quadratic nonresidue
  6. (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.
  7. (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
  8. Conditionally bounding analytic ranks of elliptic curves. in ANTS X: Proceedings of the Tenth Algorithmic Number Theory Symposium
  9. (with Leo Goldmakher) The distribution of the maximum of character sums. Mathematika 59 (2013), no. 2, 427–442.
  10. (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
  11. (with Jason Bell) Bounded step functions and factorial ratio sequences. International Journal of Number Theory 5 (2009), no. 8, 1419--1431.
  12. Factorial ratios, hypergeometric series, and a family of step functions. Journal of the London Mathematical Society (2) 79 (2009), no. 2, 422--444.