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[TMS] On Schmidt's games, badly approximable numbers & winning sets

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If you have a question about this talk, please contact Jason Kwong.

Schmidt introduced a simple and powerful way to study certain important sets of real numbers, that although they exhibit remarkable rigidity features, they are ‘too thin’ to be detected using classical methods in analysis. The set of real numbers which badly approximable by rationals is an important example of such a set. In this talk, we will discuss Schmidt’s games, their applications and generalisations in geometry and dynamics. As a warm-up for the talk, you might like to try the following problem: Is every real number the difference of two badly approximable numbers? [1]

This talk is part of the Trinity Mathematical Society series.

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