TCC Course (Autumn 2010)

Dynamical Systems in Number Theory

Course Objectives: In this course we discuss some of the results and conjectures in number theory that can be approached using techniques from the theory of dynamical systems. For instance, we consider the following questions:

It turns out that all these deep questions are intimately related to distribution of orbits of suitable dynamical systems. While this is also a difficult problem on its own right, there has been several recent breakthroughs in the field that we shall discuss. In particular, one of the highlights of the course will be Ratner's theorems about the properties of unipotent flows and their applications to number theory.

The subject of the course lies on crossroads between the theory of dynamical systems and number theory. However, we assume only minimal background in these fields and rely mostly on basic knowledge of analysis and algebra.

We plan to cover some of the following topics:

Time: Monday 2-4pm; See TCC Timetable

Lecture notes:

Homework Problems:

Course Assessment: The course will be assessed by problem sheets that will be posted here.