Speaker: 
Paul Baginski Undergraduate Honors Student Department of Mathematical Sciences Carnegie Mellon University 

Title:  The JetSpaces Proof of the MordellLang Conjecture 
Abstract:
In 2001, Anand Pillay and Martin Ziegler proposed an alternate modeltheoretic proof to the MordellLang Conjecture in characteristic zero. Their proof followed many of the steps of Hrushovski's construction, however the proofs diverged at one key step. Whereas Hrushovski used deep modeltheoretic results about Zariski geometries, Pillay and Ziegler utilized a natural generalization of differential tangent spaces, called differential jet spaces. In this talk, I will transfer the statement of the MordellLang conjecture given in my previous lecture to a second "relative form" which is amenable to modeltheoretic methods. I will then provide an outline of the key steps in the jet spaces proof of the relative form of the theorem. In particular, I will develop the idea of a jet space and discuss how Pillay and Ziegler employed them to obtain key modeltheoretic information.