Paul Fili

Associate Head and Associate Professor

Department of Mathematics

My Contact Info

Office: MSCS 532
Office hours: Office hours for each of my courses is listed on the Canvas page.
E-mail: paul.fili (at)


In the Spring of 2023, I am teaching Math 4753/5753: Introduction to Cryptography. 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. I am interested in Bogomolov and Lehmer type problems for heights, unlikely intersections, and equidistribution for dynamical systems. Lately I've become interested in stochastic dynamics.



Unpublished notes

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

Graduate students

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

About me

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.