Course details
Semester
 Autumn 2021
 Monday, October 4th to Friday, December 10th
Hours
 Live lecture hours
 10
 Recorded lecture hours
 0
 Total advised study hours
 40
Timetable
 Fridays
 13:05  13:55
Course forum
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Description
It is often the case that the mathematical objects we are interested in, both those to be classified and the intended invariants, can be encoded by real numbers. In this case the question of classifiability boils down to the existence of a "reasonably definable" map from R to R respecting the equivalence relations. Taking "Borel" as a suitably liberal interpretation of "reasonably definable", we can sometimes prove that no such map exist, ruling out the classification. This has been successfully used to prove that some old classification programmes, in areas such as C*algebras and ergodic theory, were impossible tasks.
This course will introduce students to this area, developing the theory from theground up, culminating in Hjorth's notion of turbulence, which is the central tool for proving unclassifiability results.
Prerequisites
Syllabus
Lecturer

Dr Andrew BrookeTaylor
 University
 University of Leeds
Bibliography
Follow the link for a book to take you to the relevant Google Book Search page
You may be able to preview the book there and see links to places where you can buy the book. There is also link marked 'Find this book in a library'  this sometimes works well, but not always  you will need to enter your location, but it will be saved after you do that for the first time.
Assessment
The assessment for this course will be released on Monday 10th January 2022 and is due in by Sunday 23rd January 2022 at 23:59.
Assessment for all MAGIC courses is via takehome exam which will be made available at the release date (the start of the exam period).
You will need to upload a PDF file with your own attempted solutions by the due date (the end of the exam period).
If you have kept uptodate with the course, the expectation is it should take at most 3 hours’ work to attain the pass mark, which is 50%.
Please note that you are not registered for assessment on this course.
Lectures
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