# Basic Notions: Kobi Peterzil (U. of Haifa) "The Pila-Zannier method: applications of model theory to Diophantine geometry".

## Location:

A family of problems in Diophantine geometry has the following

form: We fix a collection of "special" algebraic varieties among which the

0-dimensional are called "special points". Mostly, if V is a special variety

then the special points are Zariski dense in V, and the problem is to prove

the converse: If V is an irreducible algebraic variety and the special

points are Zariski dense in V then V itself is special.

Particular cases of the above are the Manin-Mumford conjecture