Alice Medvedev : rational dynamics and the model theory of difference fields

Posted by , part of the Logic Seminar.

At

March 17, 2008, 4 p.m.

In

SEO 427

Abstract

Consider the following rational dynamical system: $V$ is an affine space, and $F: V \rightarrow V$ acts polynomially coordinate-wise: $F(x, y, \ldots, z) = f(x), g(y), \ldots, h(z))$ for polynomials $f, g, \ldots, h$. What subvatieties of $V$ are invariant under this action? In a model of ACFA, consider a union $S$ of definable minimal sets $S_i := \{ x: \sigma(x) = f_i(x) \}$ for some polynomials $f_i$. What is the pregeometry on $S$ given by the model-theoretic algebraic closure operator? This is the same question, and I have an answer.

Tea at 4, talk shortly thereafter.