One of the most exciting areas in analysis today is the rapidly emerging new topic of additive combinatorics. Building on Gowers' use of the Freiman-Ruzsa structure theorem in harmonic analysis (in particular, in his proof of Szemeredi's theorem), Green and Tao famously proved that there are arbitrarily long arithmetic progressions of primes, and Bourgain has given non-trivial estimates for hitherto untouchably short exponential sums. This new area involves harmonic analysis, ergodic theory, discrete geometry, combinatorics, probability theory and number theory, and this conference will include an eclectic mix of participants, among them most of the key players in the field who will present the new directions and developments, such as **J. Bourgain** (IAS, Princeton), **T. Gowers** (Cambridge), **B. Green** (Bristol), **I. Ruzsa** (Alfred Renyi Institute) and **T. Tao.** This workshop will immediately follow the CRM-Clay School on Additive Combinatorics. |