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

职务名称：RIMS-UCI关于模退化的算术应用的合作会议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行的研讨会。 讲座结合联合收割机代数和复杂的解析几何给新的见解到集合的代数关系，从完善的参数（模数）空间。一些讲座介绍了一个新的动物园的尖点类型。这些推广了附加到模曲线的尖点。他们提取什么支配以前微妙的问题，并加强成熟的主题，如德利涅的切线基点和贝利覆盖。 回火的基本群体，模块塔和尖嵌入曲线在他们的雅可比出现在特色讲座。数论学家和代数几何学家将发现结果远远超出了以前的研讨会在京都，2002年10月在RIMS研究所。特别是，有新的应用程序，以激励学生和博士后学习技术，从他们的坏减少类型的代数方程分类。受邀的演讲者，和一个顶峰卷到以前的出版物系列，将吸引新的博士。学生该项目支持美国参与者参加2003年5月7日至10日在加州大学欧文分校举行的研讨会。用方程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过滤出除本质之外的所有内容。这次研讨会是继2002年10月在京都的RIMS研究所举行的技术性更强的研讨会之后举行的。我们的演讲者将强调基于尖点几何的数据过滤过程的重要新贡献。伊夫·安德烈的系列讲座和其他受邀演讲者的重点讲座将吸引新的博士学位。学生到外地。他们将学习新的想法来分类方程的不良约简类型。应用将是一个广泛的主题，包括弦理论和高度措施。一份会议记录将作为一个顶点将结果分发给以前的一系列相关出版物。

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.