Free resolutions and computations, Berkeley 2017

该奖项支持参加将于2017年7月17日至21日在加州大学伯克利分校举行的题为“Stillman's Conjecture and other Progress on Free Resolution”的会议和软件开发研讨会。本次会议的核心重点是两个重要而及时的研究领域。会议将在令人兴奋的发展和新突破的时刻汇集领先的专家和年轻的研究人员。 许多这些最近的发展受到计算机实验的启发，这些实验在代数几何和交换代数领域变得越来越普遍。 研讨会将重点开发Macaulay 2，这是这些领域中领先的计算机代数系统。 通过帮助研究人员开发自己的软件包，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。 这些例子可以回答老问题，激发新想法，就像那些将在科学会议上提出的问题一样。更多的信息可以在会议网站上获得：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。这样一个会议的时机已经成熟;在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年前的关于自由决议的猜想。也有最近的进展Stillman的问题，要求一个约束的投影尺寸的理想，完全基于数量的发电机和程度（梅尔Hochster和克雷格Huneke将给会谈他们的工作）。会议随后将转向Macaulay 2的软件开发研讨会，Macaulay 2是世界领先的支持交换代数和代数几何研究的软件系统之一。Macaulay 2是开源的，它扩展其功能的关键方法之一是通过包，这允许研究人员编写利用Macaulay 2核心功能的函数。该研讨会将通过构建随后将被整合到Macaulay 2的软件包来加强研究基础设施。它也将作为一个培训基地代数使用和编写麦考利2。该研讨会将建立桥梁，并促进工人之间的自由决议的理论和计算方面的联系。Macaulay 2研讨会有着包容性的历史，既包括代表性不足的群体，也包括来自各种各样职位的参与者。 组织者致力于延续这一传统。

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.