$ \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.

Data:

Papers:

  1. Averages of character sums
  2. (with Leo Goldmakher) Pólya-Vinogradov and the least quadratic nonresidue
  3. (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.
  4. (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
  5. Conditionally bounding analytic ranks of elliptic curves. in ANTS X: Proceedings of the Tenth Algorithmic Number Theory Symposium
  6. (with Leo Goldmakher) The distribution of the maximum of character sums. Mathematika 59 (2013), no. 2, 427–442.
  7. (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
  8. (with Jason Bell) Bounded step functions and factorial ratio sequences. International Journal of Number Theory 5 (2009), no. 8, 1419--1431.
  9. Factorial ratios, hypergeometric series, and a family of step functions. Journal of the London Mathematical Society (2) 79 (2009), no. 2, 422--444.

Some things I am currently working on:

Some courses I've taught:

Math 116, Winter 2008, Section 13

Math 115, Fall 2007, Section 38

Math 115, Fall 2006