### March 30 – April 5, 2006

Centre de recherches mathématiques

**Organizers **:** Jozsef Solymosi **(UBC), **Andrew Granville** (Montréal) and **David Ellwood** (Clay)

Additive combinatorics is one of the most exciting areas in mathematics today, involving ideas from number theory, harmonic and functional analysis, ergodic theory, combinatorics, probability theory and discrete geometry. The school will give the background in these areas to help the students begin to appreciate some of the recent spectacular theorems, such as the result of Green and Tao that there are infinitely many k-term arithmetic progressions of primes and Bourgain's bounds on exponential sums.

This school is intended to give to graduate students, postdoctoral fellows and junior faculty an opportunity to participate in these new developments.

**Introductory lecturers **:

**Jozsef Solymosi** (UBC) and **Andrew Granville** (Montréal)

**Key Lecturers** :

**Ben Green **(Bristol) : “Quadratic Fourier snalysis”

**Bryna Kra** (Northwestern) : “Ergodic methods in combinatorial number theory”

**Terry Tao** (UCLA) : “Combinatorial and ergodic techniques for proving Szemeredi-type theorems"

**Van H. Vu **(UCSD) : “Structure of sumsets and applications”

**Guest lecturers** :

**Tim Gowers** (Cambridge), **Imre Ruzsa** (Alfréd Rényi Institute)