We explore environments in which rigid structural information can be deduced from rather soft combinatorial hypotheses. There will be a particular focus on finite and quantitative questions, although an important aspect of the workshop will be to explore connections with corresponding infinite and qualitative questions in ergodic theory, where as a general rule more is known. Topics include (but are not be limited to) the following.

1. Freiman's theorem concerning the structure of sets with small doubling;
2. The Gowers Inverse Conjecture, concerning the structure of sets containing many parallelepipeds;
3. Finite versions of Ratner's theorem, concerning the structure of finite unipotent orbits in dynamical systems.

Accommodations: A block of rooms has been reserved at the Rose Garden Inn. Reservations may be made by calling 1-800-992-9005 OR directly on their website. Click on “Reservations and Availability” then click on “Corporate” at the bottom of the screen and enter the word “math”. Enter Group Code CGMS67 in the “Guest Comment” box, and provide requested information The cut-off date for reservations is October 17, 2008. A block of rooms has been reserved at the Hotel Durant. Please mention the workshop name and reference the following code when making reservations via phone, fax or e-mail: BQ0000. The cut-off date for reservations is October 3, 2008.