
CMS CoxeterJames Lecture / Conférence CoxeterJames de la SMC (Organizers)
 DAMIEN ROY, Department of Mathematics and Statistics, University of Ottawa,
Ottawa, Ontario K1N 6N5
Results and methods of transcendental number theory

Although the ancient Greeks knew the existence of irrational numbers,
the theory of transcendental numbers is only about 150 years old. It
was born in 1844 when Liouville established, for the first time, the
existence of transcendental numbers. Since then, the recent advances
of the theory, especially around Baker's theorem on linear forms in
logarithms, have proved useful in many areas of number theory, in
particular for solving Diophantine equations. This talk will focus on
the transcendence properties of values of the usual exponential
function. We will sketch the present state of knowledge on this topic
and describe some of the tools that are involved in the proofs,
pointing out open questions and potential avenues for further
progress.

