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.

该奖项支持参加将于2017年7月17-21日在加州大学伯克利分校举行的题为《斯蒂尔曼猜想和自由解析的其他进展》的会议和软件开发研讨会。本次会议的一个核心重点是两个重要和及时的研究领域。在这个令人振奋的发展和新的突破之际，这次会议将把领先的专家和年轻的研究人员聚集在一起。最近的许多发展都是受到计算机实验的启发，计算机实验在代数几何和交换代数领域变得越来越常见。研讨会的重点将是开发Macaulay2，这是这些领域内领先的计算机代数系统。通过帮助研究人员开发他们自己的软件包，当他们和其他人计算推动数学前沿的新例子时，将立即产生研究影响。这样的例子可以回答旧的问题，激发新的想法，就像那些将在科学会议上提出的一样。更多信息可在会议网站上获得：https://macaulay2.github.io/Workshop-2017-Berkeley/The会议的前两天将是一个关于自由决议和交换代数的会议。召开这样一次会议的时机已经成熟；2016年夏天，Irena Peeva和Jason McCullough(两人都将在会议上发言)解决了一个著名的38年前关于自由决议的猜想，这是由于Eisenbud-Goto。斯蒂尔曼的问题最近也取得了进展，该问题要求仅根据生成元的数量和学位来确定理想的射影维度的界限(梅尔·霍奇斯特和克雷格·亨克将就他们的工作发表演讲)。然后，会议将转向Macaulay2的软件开发研讨会，Macaulay2是支持交换代数和代数几何研究的世界领先软件系统之一。Macaulay2是开源的，它扩展功能的关键方式之一是通过包，这允许研究人员编写利用Macaulay2的S核心函数的函数。讲习班将通过编制一揽子计划来加强研究基础设施，这些计划随后将纳入Macaulay2。它还将作为代数学家使用Macaulay2和编写Macaulay2的培训基地。研讨会将在自由解决方案的理论和计算方面搭建桥梁并促进工作人员之间的联系。Macaulay2讲习班具有包容性的历史，既包括代表性不足的群体，也包括来自各种不同立场的参与者。主办方致力于延续这一传统。