Department of Mathematics
My Contact Info
Office: MSCS 532
Office hours (online): For Math 4023/5073, Wednesday 2:30-3:20 pm, Thursday 5:00-5:50 pm; for Math 2163, Thursday 4:00-4:50 pm, Friday 1:00-1:50 pm; and by appointment.
E-mail: paul.fili (at) okstate.edu
In the Fall of 2020, I am teaching Math 2163: Calculus III, and Math 4023/5073: Introduction to Analysis. Course pages are available on Canvas.
My research interests are in number theory and analysis. I am primarily interested in topics relating to the distribution of algebraic numbers and points of small height, potential theory, and arithmetic dynamics. My work is focused on Bogomolov and Lehmer type problems as well as unlikely intersections for dynamical systems.
- 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.
Here is my doctoral thesis, Orthogonal decomposition of the space of algebraic numbers modulo torsion from the University of Texas at Austin (May 2010).
My Curriculum Vitae.
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 Sept. 1, 2020.