In the Spring of 2023, I am teaching Math 4753/5753: Introduction to Cryptography. Course pages are available on Canvas.

- Stochastic Equidistribution and Generalized Adelic Measures (with J. Doyle and B. Tobin), preprint. A revision is coming soon! You can find pictures of Stochastic Julia sets and more here and slides from a recent talk here.
- A metric of mutual energy and unlikely intersections for dynamical systems, preprint. Revision in progress.

- Dynatomic polynomials, necklace operators, and universal relations for dynamical units (with J.R. Doyle and T. Hyde), New York J. Math.
**28**(2022), 534–556. - Wandering points for the Mahler measure (with L. Pottmeyer and M. Zhang), Acta Arith.
**204**(2022), no. 3, 225-252. - On the behavior of Mahler's measure under iteration (with L. Pottmeyer and M. Zhang),
*Monatshefte für Mathematik***193**(2020), 61–86. - Quantitative height bounds under
splitting conditions (with L. Pottmeyer), Trans. of the Amer.
Math. Society,
**372**(2019), no. 7, 4605-4626. - Energy integrals and small points for the Arakelov
height (with C. Petsche and I. Pritsker), Archiv der Mathematik,
**109**(2017), no. 5, 441-454. - Height bounds for algebraic numbers
satisfying splitting conditions (with I. Pritsker), J. Number Theory,
**175**(2017), 250-264. - Equidistribution and the heights of totally real and totally
*p*-adic numbers (with Z. Miner), Acta Arith., vol. 170, no. 1 (2015), 15-25. - Energy integrals over local fields and global height bounds (with C. Petsche), Int. Math. Res. Not. 2015(5): 1278-1294, 2015.
- On the heights of totally
*p*-adic numbers, J. Théor. Nombres Bordeaux 26(1): 103-109, 2014. - A generalization of Dirichlet's unit theorem (with Z. Miner), Acta Arith., 162(4): 355-368, 2014.
- Norms extremal with respect to the Mahler measure (with Z. Miner), J. Number Theory, 132(1): 275-300, 2012.
- Orthogonal decomposition of the space of algebraic numbers and Lehmer's problem (with Z. Miner), J. Number Theory, 133(11), 3941-3981, 2013.
- On the non-Archimedean metric Mahler measure (with C.L. Samuels), J. Number Theory, 129: 1698--1708, 2009.

- On totally real numbers and equidistribution (with Z. Miner).

Here is my doctoral thesis, Orthogonal decomposition of the space of algebraic numbers modulo torsion from the University of Texas at Austin (May 2010).

I currently have one Ph.D. student, Preston Kelley.

My Curriculum Vitae (updated Fall 2022).

I received my bachelor's degree in Mathematics and Physics with a language citation in Classical Greek from Harvard University in 2004. I wrote my senior honors thesis on Lenstra's Elliptic Curve method of factorization under the direction of Frank Calegari. I received my Ph.D in Mathematics in May 2010 at the University of Texas at Austin studying under the supervision of Jeffrey Vaaler.

Last updated Feb. 1, 2023.