Department of Mathematics
Colloquium
by
Swanlund Prof. Anand Pillay

I will first discuss the basic objects and problems of contemporary model theory, in the light of the history of modern logic. I will then discuss the relevance of these notions to other areas of mathematics, both as an explanatory tool as well as through yielding new theorems. I will try to touch on one or two of the following topics: rigidity theorems in Lie groups, strong approximation in arithmetic groups, diophantine questions in algebraic geometry.

For background and an introduction to the subject:

(1) "The Model Theory of Groups", edited by Nesin and Pillay, Notre Dame Press, (First chapter)

(2) "Model Theory of Fields", by Marker, Messmer and Pillay, Lecture Notes in Logic 5, Springer-Verlag, (First chapter)