Fri Dec 5, 2008
60 Evans Hall, 4:10–6 PM
Thomas Scanlon (University of California, Berkeley)
Algebraic Dynamics and the Model Theory of Difference Fields
In algebraic dynamics, one studies the properties of repeated application of rational functions while the work on the model theory of difference fields concerns the structure of the definable sets in fields considered in the language of rings augmented by a function symbol for a distinguished automorphism, but there are deep connections between the two subjects. I will discuss several of these connections including a dynamical consequence of Hrushovski’s theorem on the nonstandard Frobenius due to Poonen, some results on descent of algebraic dynamical systems due to Chatzidakis and Hrushovski, and some theorems on the arithmetic of polynomial dynamical systems due to Medvedev and myself.