Undergraduate Honors Student
Department of Mathematical Sciences
Carnegie Mellon University
|Title:||The Mordell-Lang Conjecture in characteristic zero|
The Mordell-Lang conjecture has played an important role in Model Theory since E. Hrushovski's model-theoretic proof of it in 1996. Since then, there have been no non-model-theoretic proofs given of the conjecture in full generality. Therefore, the Mordell-Lang conjecture has stood fast as a testament to the applicability of Model Theory to other fields. In this first lecture, I will provide a primer on the Mordell-Lang conjecture in characteristic zero. The conjecture will be traced back to its diophantine roots, and then abstracted to its modern statement. In the process I hope to an idea of the motivation behind the conjecture, and its significance in number theory and algebraic geometry.