Logic Seminar
Jonathan Kirby
UIC
The model theoretic geometry of exponentiation
Abstract: The complex field with exponentiation is a structure about which surprisingly little is known. Zilber
conjectured that it is isomorphic to the "pseudoexponentiation" he constructed using Hrushovski's
amalgamation technique. This conjecture is very hard, because it implies Schanuel's conjecture of
transcendental number theory and would give a complete description of the algebraic relations between
exponentials.
However, Zilber's conjecture can be separated into this difficult number-theoretic part and a geometric
part. I will describe how the geometric part is related to the model theory of differential fields, and
will outline the progress towards proving it.
Tuesday October 17, 2006 at 4:00 PM in SEO 427