Logic Seminar
Alice Medvedev
UIC
Model theory of difference fields: connections to algebraic geometry and rational dynamics
Abstract: A difference field is a field with a distinguished automorphism
$\sigma$; for example, one can look at a field of characteristic $p$
and take $\sigma(x) = x^p$ to be the Frobenius automorphism.
Model-theorists have things to say about the class of
existentially-closed difference fields: it is first-order
axiomatizable, and the resulting theory, called ACFA, is supersimple
and generally nice. I will say things certain minimal definable sets
in ACFA, namely about solution sets of $\sigma(x) = f(x)$ for rational
functions $f$.
Tuesday October 16, 2007 at 4:00 PM in SEO 427