Metric Number Theory (MAGIC085)
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Summary: The course is an introduction to the theory of metric Diophantine approximation. This broad and topical area of number theory combines ideas from measure theory, fractal geometry, probability theory, ergodic theory and dynamical systems. Even at the introductory level, the theory of metric Diophantine approximation naturally illustrates the interplay of different branches of mathematics. A particular goal of the course is to bring to the forefront the classical and recent `transference' principles that `link' various aspects of the general theory. For example, the classical Khintchine transference principle provides a link between the homogeneous and inhomogeneous theories. On the other hand, the recent Mass Transference Principle provides a link between the Lebesgue and Hausdorff measure theories. Another key goal is to discuss current topical areas of research. This will involve discussing the fundamental conjectures of Littlewood and Schmidt in the theory of simultaneous Diophantine approximation.
Autumn 2019 (Monday, October 7 to Friday, December 13)
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The assessment for this course will be via a single take-home paper in January with 2 weeks to complete and submit online. There will be 3-4 questions. A pass will be awarded to any script which is judged to be correct on at least half of the questions set.
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