Metric Number Theory (MAGIC085) |
GeneralDescription
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.
Topics from:
Useful texts:
SemesterAutumn 2017 (Monday, October 9 to Friday, December 15) Timetable
PrerequisitesPrerequisites:
SyllabusTopics from:
Lecturers
BibliographyNo bibliography has been specified for this course. AssessmentNo assessment information is available yet.
No assignments have been set for this course. FilesFiles marked L are intended to be displayed on the main screen during lectures.
Recorded LecturesPlease log in to view lecture recordings. |