COURSE DESCRIPTION: This will be a new course different from other model theory courses I offered in the past. The most important applications of mathematical logic to classical mathematics are recent results of Ehud Hrushovski (solutions for the Mordell-Lang conjecture for function fields and an effective bound for The Manin-Mumford conjecture). It turns out that the applications depend in an essential way on a significant body of pure model theory that was developed by Hrushovski extending and building on already deep work of Saharon Shelah and Boris Zilber. The course will concentrate in the new aspects of model-theory necessary for the above results. The field is called geometric model theory it was originated by Zilber to get a fine analysis of the structure of the category of models of a totally categorical first-order theory and turned out to be useful for much more general (and special) results.

PREREQUISITES: Little more than an elementary course in model theory (21-603), familiarity of the basic parts of my papers "A primer of simple theories" and "The D-rank is equal to the R-rank" will also be assumed. I suppose that the student had a graduate course in algebra. In case you don't have the above prerequisites and is eager to take this course I suggets that you will get my permission first.

BOOKS: There is no official text, the following sources are relevant:

• Elisabeth. Bouscaren, Model Theory and Algebraic Geometry, An introduction to E. Hrushovski's proof of the geometric Mordell-Lang conjecture, Lecture Notes in Mathematics #1696, Springer-Verlag, 1998.
• Anand Pillay, Geometric Stability Theory, Oxford Univ. Press 1996.
  For price comparison click here.
• John T. Baldwin. Fundamentals of Stability Theory. Springer-Verlag,1988. price comparison.
• Steve Buechler. Essential Stability Theory. Springer-Verlag, 1996. price comparison.
• Saharon Shelah, Classification Theory and the Number of Nonisomorphic Models, Rev. Ed., North-Holland, 1990. price comparison.

Evaluation: Will be based on a final (3 hours written examination) and a 50 minutes midterm.