Free resolutions and computations, Berkeley 2017

免费分辨率和计算，伯克利 2017 年

• 批准号: 1701922
• 负责人: Branden Stone
• 金额: $ 3万
• 依托单位: Adelphi University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2017
• 资助国家: 美国
• 起止时间: 2017-05-01 至 2018-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1701922&HistoricalAwards=false
• 关键词: Free; resolutions; computations; Berkeley; 2017

This award supports participation in the conference and software development workshop entitled "Stillman's Conjecture and other Progress on Free Resolution" to be held on July 17-21, 2017, at the University of California, Berkeley. A core focus for this meeting is two important and timely areas of research. The conference will bring together leading experts with young researchers at a time of exciting developments and new breakthroughs. Many of these recent developments were inspired by computer experiments, which are becoming more common within the fields of algebraic geometry and commutative algebra. The workshop will focus on developing Macaulay2, a leading computer algebra system within these fields. By helping researchers develop their own packages, there will be immediate research impact as they and others compute new examples which push the mathematical frontier. Such examples can answer old questions and inspire new ideas, just like those that are to be presented at the scientific conference. Further information is available at the conference website: https://macaulay2.github.io/Workshop-2017-Berkeley/The first two days of the meeting will be a conference on free resolutions and commutative algebra. The time is ripe for such a conference; in Summer 2016 Irena Peeva and Jason McCullough (both of whom will speak at the meeting) resolved a famous 38-year-old conjecture on free resolutions due to Eisenbud-Goto. There has also been recent progress on Stillman's question, which asks for a bound on projective dimension of an ideal, based solely on the number of generators and degrees (Mel Hochster and Craig Huneke will give talks on their work). The meeting will then switch gears, to a software development workshop for Macaulay2, one of the world's leading software systems for supporting research in commutative algebra and algebraic geometry. Macaulay2 is open source, and one of the key ways in which it extends its functionality is through packages, which allow researchers to write functions that utilize Macaulay2's core functions. The workshop will enhance research infrastructure by constructing packages which will be subsequently integrated into Macaulay2. It will also serve as a training ground for algebraists to use and write for Macaulay2. The workshop will build bridges and foster connections between workers on the theoretical and computational aspects of free resolutions. Macaulay2 workshops have a history of being inclusive both in terms of including underrepresented groups and for including participants from a wide variety of positions. The organizers are committed to continuing this tradition.

该奖项支持将于2017年7月17日至21日在加利福尼亚大学伯克利分校举行的题为“ Stillman的猜想和其他自由解决方案进展”的会议和软件开发研讨会。这次会议的核心重点是两个重要及时的研究领域。会议将在激动人心的发展和新突破时与年轻的研究人员召集领先的专家。 这些最近的发展中的许多是受计算机实验的启发，这些实验在代数几何和交换代数的领域变得越来越普遍。 研讨会将重点介绍开发MacAulay2，这是这些字段中领先的计算机代数系统。 通过帮助研究人员开发自己的包装，随着他们和其他人计算出推动数学前沿的新示例，将会产生立即的研究影响。 这样的例子可以回答旧问题并激发新想法，就像在科学会议上呈现的那些想法一样。会议网站上提供更多信息：https：//macaulay2.github.io/workshop-2017-berkeley/会议的前两天将是一次免费决议和交换代数会议。这样的会议已经成熟了。在2016年夏季，Irena Peeva和Jason McCullough（两者都会在会议上讲话）由于Eisenbud-Goto而在免费决议中解决了一个著名的38岁猜想。 Stillman的问题最近也取得了进展，该问题仅基于发电机和学位的数量，要求对理想的投影维度进行束缚（Mel Hochster和Craig Huneke将就他们的工作进行谈判）。然后，会议将把齿轮转换为Macaulay2的软件开发研讨会，这是世界领先的软件系统之一，用于支持通勤代数和代数几何学研究。 MacAulay2是开源，它扩展其功能的关键方法之一是通过软件包，这使研究人员能够编写利用MacAulay2的核心功能的功能。该研讨会将通过构造随后集成到Macaulay2的包装来增强研究基础架构。它还将作为代数主义者使用和写作MacAulay2的训练场。该研讨会将在工人之间建立桥梁，并在自由决议的理论和计算方面建立联系。 Macaulay2研讨会在包括代表性不足的群体以及包括各种职位的参与者中都具有包容性的历史。 组织者致力于继续这一传统。