Math 711 — The Arithmetic of Dynamical Systems — Winter 2010
Instructor: Michael Zieve
|Office: 3835 East Hall
||Office Hours: 2:30–4 (T, Th) or by appointment
||Class: T, Th 1–2:30 in 3088 East Hall
This course provides an introduction to
a recently developed
area of mathematics combining
It addresses number-theoretic aspects of orbits of polynomials
(such as integrality and rationality questions), dynamics over
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
The main prerequisite is fluency in the language of
and Galois theory, at the level of Math 593/594.
We will also use basic concepts from
algebraic number theory
(rings of integers,
but students can learn these during the course.
Related activities January–June 2010:
Special session on arithmetic dynamics at the
AMS/MAA Annual Meeting
in San Francisco in January.
Arizona Winter School in Number Theory (March 13–17)
focuses on Number Theory and Dynamics. 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.
In this year's
Michigan Lectures in Number Theory
Matt Baker explains
applications of potential theory on the
Berkovich projective line to problems in arithmetic dynamics.
The Bellairs Workshop in Number Theory (May 2–9)
in Barbados addresses moduli spaces in arithmetic dynamics.
Laura DeMarco is organizing a conference on
the arithmetic of complex dynamics at the
University of Illinois at Chicago, May 17–21.
There is an algebraic dynamics workshop at the CUNY Graduate Center,
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