CONFERENCE: Tutorials in Applicable Algebraic Geometry

最近有一个显着增加的应用方法的代数几何的问题以外的数学。 由此产生的跨学科工作必然需要代数几何专家和其他学科的专家之间的互动。 PI将于2013年7月29日至31日举办一个研讨会，重点介绍非专家的两个基本工具植根于代数几何：数值代数几何和复曲面几何。 作者最近的书籍在这两个领域将讲课：弗兰克索蒂尔和乔纳森豪恩斯坦的数值代数几何，约翰利特尔和哈尔申克的复曲面几何。 这些讲座将作为这两个领域的方法和软件的快速介绍，重点是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的Pingree Park山校区举行。应用领域的数学问题有时可以转化为某类问题，即多项式系统。 多年来，没有有效的方法来解决多项式系统，因此研究人员不得不为他们的问题找到不同的，有时不太理想的公式。 然而，随着最近的发展，在数值代数几何和复曲面几何，它现在是合理的，以解决相对较大的多项式系统直接。 这些新的计算工具为研究以前难以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制的能力。 该奖项支持的研讨会将有助于加快需要这些强大新工具的研究人员的使用。

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.