Second RIMS-UCI Collaboration Conference: Arithmetic Applications of Moduli Degeneration; May 7-10, 2003; Irvine, CA

RIMS-UCI模退化算术应用合作会议该项目支持美国与会者参加2003年5月7日至5月10日在加州大学欧文分校举行的研讨会。这些讲座结合了代数和复杂的解析几何，从精化的参数(模)空间给出了对代数关系集合的新见解。一些讲座介绍了一个新的尖点类型的动物园。这些曲线泛化了附加到模曲线上的尖点。它们提取了管理以前微妙问题的内容，并增强了成熟的主题，如Deligne的切线基点和Belyi覆盖。经过锻炼的基本群、模塔和曲线的尖点嵌入其雅可比线出现在专题讲座中。数论学家和代数几何学家将发现，结果远远超过2002年10月在京都举行的RIMS研究所的研讨会。特别是，有了新的应用来激励学生和博士后学习将代数方程从糟糕的归约类型中分类的技术。受邀的演讲者，以及前一系列出版物的顶峰卷，将吸引新的博士生。该项目支持美国参与者参加2003年5月7日至5月10日在加州大学欧文分校举办的研讨会。用方程式描述的数学对象可能非常复杂，充满了人们想要消除的外围数据。这些对象的参数空间上的特殊结构可以帮助研究人员从这些方程中筛选出除本质之外的所有内容。这次研讨会是继2002年10月在京都RIMS研究所举办的更技术性研讨会之后举行的。我们的演讲者将强调对这一基于尖点几何的数据过滤过程的重大新贡献。Yves Andre的系列讲座和其他受邀演讲者的重点演讲将吸引新的博士生进入该领域。他们将学习根据不好的约化类型对方程进行分类的新想法。应用范围很广，包括弦理论和高度测量。会议论文集将作为以前一系列相关出版物的顶峰来传播成果。

Title: RIMS-UCI Collaboration Conference on Arithmetic Applications of Moduli Degeneration This project supports US participants to attend a workshop at UC Irvine, May 7 to May 10, 2003. The lectures combine algebra and complex analytic geometry to give new insights into collections of algebraic relations from refined parameter (moduli) spaces. Some lectures introduce a new zoo of cusp types. These generalize cusps attached to modular curves. They extract what governs previously subtle problems and enhance mature topics like Deligne's tangential base points and Belyi covers. Tempered fundamental groups, Modular Towers and cusp embeddings of curves in their jacobians appear in featured lectures. Number theorists and algebraic geometers will find results going far beyond those from a previous workshop in Kyoto, October, 2002 at RIMS Institute. Especially, there are new applications to motivate students and post-doctorals to learn techniques for classifying algebraic equations from their bad reduction types. The invited speakers, and a capstone volume to the previous publication series, will attract new Ph.D. students. This project supports US participants to attend a workshop at UC Irvine, May 7 to May 10, 2003. Mathematical objects described by equations can be painfully complicated, full of peripheral data one would like to eliminate. Special structures on parameter spaces for these objects can help researchers filter all but the essentials from these equations. This workshop follows the more technical workshop at RIMS Institute in Kyoto, October, 2002. Our speakers will emphasize significant new contributions to this data filtering process based on cusp geometry. A lecture series by Yves Andre and focused lectures by the other invited speakers will attract new Ph.D. students to the field. They will learn new ideas for classifying equations by their bad reduction types. Applications will be to a wide range of topics, including string theory and height measures. A conference proceedings will disseminate the results in a capstone to a previous series of related publications.