Math 711 - The Arithmetic of Dynamical Systems - Winter 2010


Instructor: Michael Zieve    email: zieve@umich.edu
Office: 3835 East Hall Office Hours: 12-1, 2:30-3 (T, Th)  or by appointment
Phone: 615-3650 Class: T, Th 1-2:30

This course provides an introduction to a recently developed area of mathematics combining dynamical systems and number theory. It addresses number-theoretic aspects of orbits of polynomials (such as integrality and rationality questions), dynamics over local and global fields, dynamical generalizations of number theoretic results (such as the Mordell conjecture and the uniform boundedness conjecture), and dynamics of endomorphisms of algebraic groups and associated maps.

Much of this material is in the book "The Arithmetic of Dynamical Systems" by J.H.Silverman (Springer, 2007), which is recommended but not required. This course will also include more recent (published and unpublished) results.

The main prerequisite is fluency in the language of groups, rings, fields, and Galois theory, at the level of Math 593/594. We will also use basic concepts from algebraic number theory (rings of integers, units, valuations, completions, ramification), but students can learn these during the course.


Related activities:

There will be a special session on arithmetic dynamics at the AMS/MAA Annual Meeting in San Francisco in January.

This year's Arizona Winter School in Number Theory will focus on Number Theory and Dynamics, and takes place March 13-17. This annual conference series includes lectures aimed at graduate students, but more importantly includes projects which groups of students work on with the speakers. I highly recommend them to students interested in number theory. The application deadline for students seeking funding is January 11, 2010.

Matt Baker will visit Michigan April 21-23 to give three lectures on applications of potential theory on the Berkovich projective line to problems in arithmetic dynamics.

The Bellairs Workshop in Number Theory addresses moduli spaces in arithmetic dynamics, and takes place May 2-9 in Barbados.

There will be a conference on the arithmetic of complex dynamics at the University of Illinois at Chicago, May 17-21.

There will be an algebraic dynamics workshop at the CUNY Graduate Center, June 7-11.


(Note: moving your mouse over this page will reveal hyperlinks.)