Charles L. Samuels

Personal Information

I am currently a postdoctoral research fellow at Max-Planck-Institut für Mathematik in Bonn, Germany. My fellowship lasts until July 31, 2009 at which point I will begin another postdoctoral position at Simon Fraser University and the University of British Columbia in Vancouver, Canada. I finished my Ph.D. in August 2007 under the supervision of Dr. Jeffrey D. Vaaler at the University of Texas at Austin. I worked as a lecturer in the same department for the following academic year. More detailed information is available in my vita.

Research

My research interests lie in number theory. A significant part of my work is concerned with the study of Lehmer's problem and other questions that involve giving lower bounds on the Mahler measure of polynomials with integer coefficients. Among other things, I am interested in using projective heights, heights on subspaces, heights on polynomials as well as the Weil height to solve these sorts of problems. Recently, I have become interested in certain metric versions of the Mahler measure. Please see my recent papers listed below for more information.

• The infimum in the metric Mahler measure, Canad. Math. Bull., to appear.


• On the non-Archimedean metric Mahler measure (with P. Fili), J. Number Theory, 129 (2009), 1698--1708


• Estimating heights using auxiliary functions, Acta Arith. 137 (2009), no. 3, 241--251.


• Auxiliary polynomials and height functions, Ph.D. Dissertation, The University of Texas at Austin (2007).


• The Weil height in terms of an auxiliary polynomial, Acta Arith. 128 (2007), no. 3, 209--221.


• Lower bounds on the projective heights of algebraic points, Acta Arith. 125 (2006), no. 1, 41--50.

Teaching