In Search of Transcendental Numbers

Justin Sukiennik, Visiting Assistant Professor of Mathematics, University of Puget Sound

Classifying real numbers (like, rational versus irrational) can a tricky business.  This was Joseph Liouville’s problem in 1844 when he first proved that transcendental numbers existed.  He used an approximation method which was later refined by several mathematicians.  Finally, in 1955, Klaus Roth found final best possible refinement, which led to discoveries about Diophantine equations.  In this talk, we will investigate Liouville’s initial result, examine the existence of transcendental numbers, and connect these results to Diophantine equations.

Bio: Justin graduated from the University of Rochester in 2009.  He did a post-doc at the University of Minnesota for three years and taught at Colby College, his alma mater, for three years before joining the faculty at the University of Puget Sound.  Justin's research is in algebraic number theory, specifically in Diophantine geometry and height functions.