Applications of model theory to algebra and geometry (MAGIC004) 
GeneralDescription
This will be a 10 hour "version" of what was previously given (Spring 2008, Spring 2010) as a
20 hour course.
However, I plan to be somewhat more ambitious, at the expense of leaving many details of the introductory material to be done in exercises.
Among the new aspects of the new version will be the inclusion of stability theory.
The first 5 hours will introduce model theory and stability theory, including stable groups.
The last 5 hours will concern connections and applications, largely where groups of one form or the other are involved, and will be taken from among: geometric group theory, diophantine geometry over number fields and function fields (ManinMumford, MordellLang), approximate subgroups,..
Semester
Spring 2012 (Monday, January 16 to Friday, March 23) Timetable
Students
PrerequisitesSome familiarity with first order logic would be helpful but not essential.
Syllabusbeginitemize
item textbfLectures 1 to 5: BASICS OF MODEL THEORY AND STABILITY THEORY: First order languages, structures and theories, compactness, types, saturation and homogeneity, stability, stable groups.
item textbfLecture 7 to 10: APPLICATIONS: I will cover 4 or 5 topics, explaining why and how material from the earlier lectures can give insights in areas of algebra, geometry, and number theory. More details will be given closer to the start date.
enditemize
Bibliography
Note: Clicking on the link for a book will take you to the relevant Google Book Search page. You may be able to preview the book there. On the right hand side you will 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.) AssessmentThe assessment will based on doing four assignments. Passing three out of these four assignments is required for a pass overall.
The assignments will be connected with filling in details and solving some problems related to basic material in the first past of the course, and can serve as a means for nonexperts to gain some entry into and competence in general model theory.
AssignmentsAssignment 1
Assignment 2
Assignment 3
Assignment 4
FilesFiles marked L are intended to be displayed on the main screen during lectures.
