Logic Seminar
Jonathan Kirby
UIC
The theory of exponential differential equations
Abstract: I will give a complete axiomatization of the theory of exponential differential equations in the context
of differential fields.
The axiomatization consists of a description of which systems of equations can and cannot have
solutions. It builds on James Ax's differential field version of Schanuel's conjecture of transcendental
number theory. The method works for the equations satisfied by the exponential maps of any
semiabelian variety, but in this talk I will concentrate mainly on the usual exponentiation.
The first-order nature of the axiomatization is closely related to an application in diophantine
geometry, which will be discussed more carefully in a future number theory seminar. An application of
this work to complex exponentiation was discussed at a previous seminar.
Tuesday October 31, 2006 at 4:00 PM in SEO 427