Xander Faber (CICMA)

The Arithmetic of Orbits for Quadratic Dynamical Systems

For any rational number c, consider the polynomial morphism defined by x -> x^2 + c. We will discuss some of the results and outstanding conjectures regarding the behavior of rational points in orbits for maps of this form. The talk will begin with a discussion of general algebraic and arithmetic dynamics and then proceed to this special case.