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CMS Coxeter-James Lecture / Conférence Coxeter-James de la SMC

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.

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