Visiting Assistant Professor
|Office hours:||W 3:30-5, F 2:30-4|
|E-mail:||pfili at z dot rochester dot edu|
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.
- 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.
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.