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Author: William A. Stein
Interactive Parallel Computation in Support of Research in Algebra, Geometry and Number Theory

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Interactive Parallel Computation in Support of Research in Algebra, Geometry and Number Theory


A quad-core chip

January 29 -- February 2, 2007

Mathematical Sciences Research Institute in Berkeley, CA

The Official MSRI Page on this Workshop

Schedule   |   Audio   |   Speakers   |   Organizers   |   Description   |   Format   |   Registration and Funding   |   Wiki   |   Poster


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Schedule

Invited Speakers

Organizers

Description

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.

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.

Examples of specific problems that we hope to address include:

  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:

  1. new techniques and algorithms to exploit parallelism,
  2. exposure of areas and problems that may benefit from these ideas,
  3. a strategic assessment of how best to move the state of the art forward, and
  4. a significant improvement of freely available general purpose software for mathematical research.

Format

There will be at most 3 hour-long lectures a day (+ some optional talks), and there will be plenty of time for interaction between participants. In addition, we will have several 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.

Registration and Funding

Students, recent Ph.D.'s, women, and minorities are particularly encouraged to apply. Funding awards are made typically 6 weeks before the workshop begins. Requests received after the funding deadline are considered only if additional funds become available.

Potential participants should register at the MSRI page on registration and funding. Any participant interested in giving a talk should indicate this, and include an abstract on their registration form. The deadline for applications to talk is Dec. 1, and the organizing committee will make its selection by Dec. 15. Application for financial support can also be made on the MSRI registration page; we especially encourage graduate students to apply.