Paul Fili

Visiting Assistant Professor

Office:	Hylan 820
Phone:	(585) 273-5706
Office hours:	W 3:30-5, F 2:30-4
E-mail:	pfili at z dot rochester dot edu

Teaching

In the Spring of 2013, I am teaching Math 161: Calculus I, and Math 236: Abstract Algebra.

In the Spring of 2012 I taught Math 234: Quantum computation and cryptography, a course on quantum computation and cryptography. You can find the old webpage with reading suggestions here.

Research

My research interests are in number theory. I am primarily interested in topics relating to the distribution of algebraic numbers and points of small height, dynamical heights, unlikely intersections, and Mahler measure. My work has largely focused on Bogomolov and Lehmer type problems.

Papers

On totally real numbers and equidistribution (with Z. Miner), preprint.
On the heights of totally p-adic numbers, preprint.
Equidistribution and the heights of totally real and totally p-adic numbers (with Z. Miner), preprint.
A generalization of Dirichlet's S-unit theorem (with Z. Miner), preprint.
Orthogonal decomposition of the space of algebraic numbers modulo torsion. Ph.D. thesis, UT Austin, May 2010.
Norms extremal with respect to the Mahler measure (with Z. Miner), J. Number Theory, 132 v. 1 (2012), 275--300.
Orthogonal decomposition of the space of algebraic numbers and Lehmer's problem (with Z. Miner), preprint (updated 5/6/13).
On the non-Archimedean metric Mahler measure (with C.L. Samuels), J. Number Theory, 129 (2009), 1698--1708.

About me

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.