Mathematics 542: Additive Number Theory

Fall 2008

Instructor: I. Laba (Math Bldg 200, 604-822-4457, ilaba(at)
Lectures: MWF 2-3, Math 105.
Office hours: by appointment.

Homework #1, due on Friday, 17 October 2008
Homework #2, due on Monday, 24 November 2008

The course will provide an introduction to the harmonic-analytic approach to additive number theory. We will discuss a certain group of problems at the interface of analytic and combinatorial number theory, harmonic analysis, combinatorics, ergodic theory, with ideas from other fields of mathematics also mixed in. We will start with basic discrete Fourier analysis and move quickly towards active research areas, including Szemerédi's theorem and the Green-Tao theorem. The topics will include the following: For more details on current and upcoming topics, click here.

There are no formal prerequisites, but a general familiarity with harmonic analysis, combinatorics or number theory will be useful. (The Green-Tao theorem does rely on difficult correlation estimates from analytic number theory; these will be only stated without proof.) I will try to indicate at least some of the current research directions and open problems.

Your course grade will be based on two problem sets, the first one of which will be due in mid-October and the second in late November. The problem sets and the exact due dates will be announced and posted here at least 2 weeks in advance.