MATH Seminar

Title: Rational and quadratic preperiodic points for quadratic polynomials
Seminar: Algebra
Speaker: Xander Faber of Joining IDA/CCS
Contact: David Zureick-Brown, dzb@mathcs.emory.edu
Date: 2013-09-25 at 4:00PM
Venue: W306
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Abstract: Let f be a quadratic polynomial with coefficients in a number field K. The action of f on the affine line induces a dynamical system. Many researchers have speculated on and provided evidence for uniform bounds on the number of K-rational points with finite orbit under this action: such points are called preperiodic. I will survey what is expected and what is known, and then I will describe some new contributions by myself and my collaborators John Doyle and David Krumm when K=Q or when K is a quadratic number field.