CONFERENCE: Tutorials in Applicable Algebraic Geometry

会议：适用代数几何教程

• 批准号: 1321473
• 负责人: Daniel Bates
• 金额: $ 1.55万
• 依托单位: Colorado State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2013
• 资助国家: 美国
• 起止时间: 2013-09-01 至 2014-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1321473&HistoricalAwards=false
• 关键词: CONFERENCE; Tutorials; Applicable; Algebraic; Geometry

There has recently been a significant increase in the application of the methods of algebraic geometry to problems outside of mathematics. The resulting interdisciplinary work necessarily entails much interaction between experts in algebraic geometry and those from other disciplines. The PI will run a workshop July 29-31, 2013 focused on introducing non-experts to two fundamental tools rooted in algebraic geometry: numerical algebraic geometry and toric geometry. Authors of recent books in these two areas will give lectures: Frank Sottile and Jonathan Hauenstein for numerical algebraic geometry, John Little and Hal Schenck for toric geometry. These lectures will serve as a rapid introduction to the methods and software from these two areas, focused on the value for problems coming from applications. This meeting will take place at the Pingree Park mountain campus of Colorado State University.Mathematical problems in application areas can sometimes be converted into a certain type of problem, the polynomial system. For years, there was no efficient way to solve polynomial systems, so researchers had to find different, sometimes less desirable, formulations for their problems. However, with recent developments in numerical algebraic geometry and toric geometry, it is now reasonable to solve relatively large polynomial systems directly. These new computational tools open the door to study problems that were previously too difficult to consider. For example, in kinematics, the introduction of numerical algebraic geometry has already resulted in the ability to solve long-standing problems and to discover new mechanisms with special properties. The workshop supported by this award will help to expedite the use of these powerful new tools by the researchers who need them.

最近，代数几何方法在数学以外的问题中的应用有了显着的增加。由此产生的跨学科工作必然需要代数几何专家和来自其他学科的专家之间的大量互动。PI将于2013年7月29日至31日举办一次研讨会，重点向非专家介绍两种植根于代数几何的基本工具：数值代数几何和环面几何。这两个领域新书的作者将进行演讲：弗兰克·索蒂尔和乔纳森·豪恩斯坦关于数值代数几何，约翰·利特尔和哈尔·申克关于环面几何。这些讲座将作为对这两个领域的方法和软件的快速介绍，重点关注来自应用程序的问题的价值。这次会议将在科罗拉多州立大学平利公园山区校区举行。应用领域的数学问题有时可以转化为某种类型的问题，即多项式系统。多年来，一直没有有效的方法来求解多项式系统，因此研究人员不得不为他们的问题找到不同的、有时不太可取的公式。然而，随着数值代数几何和环面几何的发展，现在直接求解相对较大的多项式系统是合理的。这些新的计算工具为研究以前太难考虑的问题打开了大门。例如，在运动学中，数值代数几何的引入已经导致了解决长期存在的问题和发现具有特殊性质的新机构的能力。由该奖项支持的研讨会将帮助需要这些工具的研究人员加快使用这些强大的新工具。