Pure Mathematics Colloquium

Damien Roy, University of Ottawa

"Diophantine curiosities"

A basic problem in Diophantine approximation is to determine how well n-tuples of real numbers can be approximated by n-tuples of rational numbers, the quality of an approximation being compared to the common denominator of its n rational components.  Another problem deals with approximation to real numbers by algebraic numbers of degree at most n for some fixed integer n.  In this talk, we present some old and some recent results related to these questions, together with conjectures and open problems.  In particular, we stress the existence of family of real numbers with unexpected properties.

MC 5501