Future directions in algorithmic number theory

March 24 to 28, 2003

at the

American Institute of Mathematics, Palo Alto, California

organized by

Hendrik Lenstra, Jonathan Pila, and Carl Pomerance

This workshop, sponsored by AIM and the NSF, is occasioned by the breakthrough result of Agrawal, Kayal and Saxena devising an unconditional, deterministic, polynomial-time algorithm for distinguishing prime numbers from composite numbers. The solution of one of the basic problems in the discipline ushers in a new era. The main objective of the workshop is to consolidate the breakthrough and explore ramifications for other fundamental algorithmic problems in number theory and finite fields. In addition the workshop will look to the future of the subject and chart directions in which developments might occur.

The workshop will differ from typical conferences in some regards. Participants will be invited to suggest open problems and questions before the workshop begins, and these will be posted on the workshop website. These include specific problems on which there is hope of making some progress during the workshop, as well as more ambitious problems which may influence the future activity of the field. Lectures at the workshop will be focused on familiarizing the participants with the background material leading up to specific problems, and there will be ample time between talks for discussions and for work to be done.

Participants include M. Agrawal, D. Bernstein, P. Berrizbeitia, M. Bhargava, D. Bleichenbacher, Q. Cheng, H. Cohen, H. Cohn, D. Coppersmith, J.-M. Couveignes, S. David, B. Edixhoven, N. Elkies, S. Gao, S. Goldwasser, N. Kayal, K. Kedlaya, A. Lauder, A. Lenstra, H. Lenstra, P. Mihailescu, S. Mueller, J. Pelosi, J. Pila, C. Pomerance, V. Rodrigues, N. Saxena, R. Schoof, V. Shoup, A. Silverberg, W. Stein, P. Stevenhagen, L. Thomas, J. Voight, F. Voloch, D. Wan, M. Watkins, A. Werner, and M. Zieve.

The application deadline to participate in this workshop has passed.

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