Algebra Seminar

Model theory is very useful in solving consistency problems in Set Theory. Recent developments, due principally to Shelah and Hrushovski, give a new way to understand algebraic geometry. Following this approach, Hrushovski was the first to prove the Mordell-Lang conjecture for function fields in all characteristics. After a brief talk on "classical model theory", I will introduce the main ideas of Stability Theory within the framework of algebraic geometry. Then, I would like to give a brief description of the class of omega-stable groups of finite Morley rank which includes algebraic groups and I will conclude by discussing some model-theoritic approaches of algebraic groups.