Intensive Workshop in 2012 for Macaulay 2 Development

该提案将为麦考利2开发强化研讨会提供支持，该研讨会将于2012年8月5日至9日在北卡罗来纳州温斯顿-塞勒姆的维克森林大学举行。大约30名研究人员将参加研讨会。主要目标是在以下三个快速发展的领域实现算法：枚举几何、数值代数几何、同调代数和代数统计。这些领域在计算生物学、数据分析、统计学和理论物理学等领域都有重要的应用。因此，我们期望通过这次研讨会开发的软件包将促进我们对多个学科的知识和理解。我们还将着重于增强Macaulay2的多线程功能。Macaulay2是一个领先的计算机代数系统，用于代数几何和交换代数的研究和教学。在这两个领域的更多领域执行日益复杂的计算的能力继续革新代数几何和交换代数的研究，以及这些领域在其他研究领域的应用广度。大多数其他相关的计算机代数系统都是基于国外的，而Macaulay2（一个领先的美国项目）的持续竞争力既取决于广泛的社区对其发展的贡献，也取决于通过密集的工作组会议支持该社区的资金。来自不同机构的有经验和新手研究人员的参与对这些讲习班的工作至关重要。对于研究生和博士后来说，这些密集的研讨会也是一个很好的机会，可以在他们的职业生涯早期提高他们的论文写作技巧，利用更资深的研究人员的经验和研究专长，并与小组分享他们自己的专业知识。年轻研究人员的大量参与也有助于Macaulay2的数学家编程基础随着时间的推移而增长。这些工作坊的旅行和住宿支持对工作坊的集约性质和澳门的未来发展至关重要2。

This proposal will provide support for an Intensive Workshop for Macaulay2 Development, to be held on August 5th-9th, 2012 at Wake Forest University in Winston-Salem, NC. Approximately 30 researchers will attend the workshop. The main objective is to implement algorithms in the following three rapidly growing areas: enumerative geometry, numerical algebraic geometry, homological algebra, and algebraic statistics. These areas have significant applications in fields as diverse as computational biology, data analysis, statistics, and theoretical physics. It is the expectation, therefore, that the packages developed through this workshop will advance our knowledge and understanding across multiple disciplines. Some emphasis will also be placed on enhancing the multithreaded capabilities of Macaulay2.Macaulay2 is one of the leading computer algebra systems for research and teaching in algebraic geometry and commutative algebra. The ability to perform increasingly complicated computations in more areas of these two fields continues to revolutionize both research in algebraic geometry and commutative algebra, and the breadth of the applications of these fields to other areas of research. Most of the other related computer algebra systems are based in foreign countries and continued competitiveness of Macaulay2, a leading United States--based program, depends on both a broad community contributing to its development and the funding to support this community through intensive workgroup meetings.The participation of both experienced and novice researchers from a variety of institutions is crucial to the work of these workshops. These intensive workshops are also a great opportunity for graduate students and postdoctoral fellows to enhance their package-writing skills early in their careers, taking advantage of the experience and research expertise of the more senior researchers as well as sharing their own expertise with the group. A strong presence from young researchers also helps the base of mathematicians programming for Macaulay2 to grow over time. Travel and lodging support for these workshops are critical to both the intensive nature of the workshop and to the future development of Macaulay2.