ABSTRACT:
 In well-behaved situations, the question of whether a system of equations can 
 be solved depends on a dimension theory. The best known examples are linear 
 equations and polynomial equations. I will show that systems of differential 
 equations based on the exponential function, and on similar equations coming 
 from algebraic groups, depend on a dimension theory. Hrushovski's 
amalgamation technique is used. There are applications to the model theory of 
the  exponential function, and to diophantine geometry questions on the 
 intersection of algebraic varieties with tori.