Workshop page at the University of Washington

The goal of this workshop is to study and formulate practical parallel algorithms that support interactive mathematical research in algebra, geometry, and number theory, and to formulate strategies to encourage implementation and testing of these ideas. For more information please go to: http://sage.math.washington.edu/msri07/ Computer manufacturers have begun delivering multiprocessor machines onto desktops; indeed, this seems to be the only means for continuing the pace of cpu power growth that we have become accustomed to. At the moment, general purpose mathematical software packages rarely exploit parallelism, and this is especially true in the areas of algebra, geometry, number theory, and combinatorics. Dramatic advances in performance will only be possible if parallelism can be harnessed in ways that are transparent to users. We hope to bring together a diverse group of mathematics and computer science researchers and students to discuss algorithms, assess current prospects, and suggest ways to move forward. Talks and discussions will cover new algorithms that exploit parallelism, specific problems likely to benefit from dramatic speedups from parallelism, and strategies to encourage implementation of these ideas. FORMAT: There will be at most 3 hour long lectures a day, and will be plenty of time for interaction between participants. In addition, we will have one or two panel discussions about the current state of the art, and strategies for implementing support for parallel computation. Before the workshop the organizers will create a preliminary strategic plan for parallel computation that will focus discussion during the workshop, and which will hopefully be significantly improved during the workshop. The talks will focus on the following topics:

1. Parallel multimodular and p-adic methods for dense, sparse and black box linear algebra over finite fields, the rational numbers and rational functions (e.g., linear system solutions, matrix multiplication, determinants and characteristic polynomials, kernels, etc.)
2. Parallel Groebner basis techniques, parallel triangular set construction
3. Distributed general purpose integer factorization algorithms
4. Uni- and multivariate polynomial arithmetic on large polynomials (high degree, many terms) such as multiplication, GCD, factorization, both for exact and approximate coefficients
5. Parallel methods for searching for rational points on curves
6. Distributed computation of large tables (e.g., elliptic curves, modular forms, data about L-functions, number fields, etc.)

Applications of parallel computation to numerical problems, e.g., in differential equations, linear algebra, etc., tend to have been more fully developed than in algebraic areas, so we will invite experts in those areas in order to hear about techniques that have been successful at attacking those problems. In sum, we aim at the following benefits for the mathematical community:   (a) new techniques and algorithms to exploit parallelism,   (b) exposure of areas and problems that may benefit from these ideas,   (c) a strategic assessment of how best to move the state of the art forward, and   (d) a significant improvement of freely available general purpose software for mathematical research.

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: P50000. The cut-off date for reservations is January 5, 2006. 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 Corporate at the bottom of the screen and when prompted enter code MATH (this code is not case sensitive). By using this code a new calendar will appear and will show MSRI rate on all room types available. The following Group Code should be entered in the "Comment" field when booking through our Website. Group Code = CGMS36. Please note: The Original Queen room type does not have an in-room T1 connection, but we do have WIFI available in our main lobby area. The cut-off date for reservations is January 8, 2007. Funding: The funding deadline has passed. Late funding requests will be considered only if additional funds become available.