Charles L. Samuels

Personal Information

I am currently a Lecturer in the Department of Mathematics at the University of Texas at Austin. I will be visiting the Max Planck Institute for Mathematics in Bonn, Germany for one year starting in August 2008. 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 height, Weil height, heights on subspaces and heights on polynomials to solve these sorts of problems. Recently, I have become interested in using heights to construct and study metrics on Abelian groups. Please see my research statement and my recent papers listed below for more information.

• (with P. Fili) On the non-Archimedean metric Mahler measure, in progress.


• Estimating heights using auxiliary functions, submitted for publication (2008).


• 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