The study of Diophantine approximation is an old one going back to antiquity. It is concerned with a quantitative study of the density of rational numbers (or more generally algebraic numbers) in the real numbers. Metric Diophantine approximation is a little younger – just over 100 years old — and is concerned with the sizes of sets of numbers having certain approximation properties.

Despite the classical nature of the problems studied, many issues remain unresolved; and the field has seen spectacular progress during the last three decades. The present project will deal with some of the remaining outstanding problems.

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