Preface The 2005 AMS Summer Research Institute on Algebraic Geometry was held at the University of Washington, Seattle, from July 25 through August 12, 2005. The advisory committee consisted of the five of us together with V. Alexeev, J. de Jong, J. Li, and K. Smith. The articles in the present volumes represent the plenary lectures, the Clay lectures, and several surveys related to seminar talks. The first week of the Institute was centered on moduli problems and the inter- actions between algebraic geometry, symplectic geometry and string theory. The topic of the second week was classical algebraic geometry with a focus on bira- tional geometry. Arithmetic geometry and characteristic p methods were taken up in the third week. The seminar organizers, V. Alexeev, D. Auroux, D. Ben-Zvi, F. Bogomolov, J. Bryan, H. Esnault, W. Fulton, N. Katz, S. Katz, K. Kedlaya, J. Koll´ ar, R. Lazarsfeld, M. Levine, J. Li, E. Miller, Y. Ruan, K. Smith, B. Siebert, Y. Tschinkel, G. Tian, B. To¨ en, and E. Viehweg, played an important role in struc- turing the scientific program. A large fraction of the participants stayed for the entire period. With a total of 513 mathematicians in attendance, Seattle 2005 was perhaps the largest algebraic geometry conference in history. We would like to thank J. Maxwell, R. Aguiar, and L. Melucci of the AMS for their work in the planning and the day-to-day organization of the Institute. The principal funding for the program came from the NSF. D. Ellwood and the Clay Institute provided crucial additional support as did DARPA and the NSA. S. Kov´ acs, T. Pantev, and R. Vakil put together an outstanding graduate student program that started before and extended for the duration of the Institute. Finally, we would particularly like to thank all the speakers and participants for their contributions to Seattle 2005. The success of the Institute was due to them. D. Abramovich, A. Bertram, L. Katzarkov R. Pandharipande, M. Thaddeus vii

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