Conference Travel Funding: "Invariant Theory and its Interactions with Related Fields"

摘要：奖项：dms -0309788首席研究员：Kathryn lesh该奖项将为参加2003年3月23日至29日在德国哥廷根举行的“不变量理论及其与相关领域的相互作用”会议（Ingo2003）的美国数学家提供部分旅费。不变量理论起源于17世纪，已被证明是数学领域的一个强大领域。在过去的50年里，它在代数拓扑、表示理论、代数几何以及许多传统领域，如数论和交换代数中找到了新的应用。Lesh教授是Ingo2003的科学组织委员会成员，Ingo2003是由阿伯丁、曼彻斯特和哥廷根的研究小组发起的，研究领域包括代数拓扑、表示理论和交换代数。这些科学家发现，跨越狭窄专业界限的交流可以带来巨大的科学效益。会议的中心主题将是不变量理论与其他领域的许多联系。在过去，围绕不变量理论主题组织的会议往往是相当专业化的，例如，集中在计算方面，或强调与大多数其他学科领域的互动，如代数拓扑。Ingo2003的组织具有更广泛的科学基础，将是全球意义上的跨学科，同时也特别关注年轻的研究人员。讨论的一些主题将包括模表示理论、协变量和“命中问题”、代数拓扑、哈希-施密特微分和微分伽罗瓦理论。不变理论的一个方面是研究变化的情况中哪些因素实际上必须保持不变的问题。例如，当地球旋转时，沿地球轴的点保持在相同的位置。磁带播放机主轴中心的点保持固定，而主轴上的其他点围绕着它转动。更令人惊讶的是，绕着圆心旋转一个圆，然后在任何一条穿过圆心的线上翻转它，必然会在固定位置留下另一条线。寻找这种情况的“不变”或“固定”元素可能是非常微妙的，它出现在各种各样的数学问题和物理应用中。2003年会议的目标是让来自不同数学学科的数学家相互学习技术，并将一门学科开发的数学工具传播到其他学科，这些学科可能会发现它们很有用。

AbstractAward: DMS-0309788Principal Investigator: Kathryn LeshThis award will provide funding to partially defray travelexpenses of U.S.-based mathematicians attending the conference"Invariant Theory and its Interactions with Related Fields"(Ingo2003), to be held in Goettingen, Germany, March 23-29,2003. Invariant theory, with roots in the 17th century, hasproven to be a robust area of mathematical endeavor. Over thecourse of the last 50 years, it has found new applications inalgebraic topology, representation theory, algebraic geometry, aswell as many traditional areas such as number theory andcommutative algebra. Professor Lesh is on the scientificorganizing committee for Ingo2003, which is an initiative ofresearch groups in Aberdeen, Manchester, and Goettingen workingin the areas of algebraic topology, representation theory, andcommutative algebra. These scientists have found thatcommunication across narrow specialty boundaries can bring greatscientific benefits. A central theme of the conference will bethe many connections of invariant theory to other fields. In thepast, conferences organized around the topic of invariant theoryhave tended to be rather specialized, for example, concentratingon computational aspects, or emphasizing interaction with at mostone other subject area, such as algebraic topology. Ingo2003 isbeing organized with a much broader scientific base and will beinterdisciplinary in a global sense, as well as having a specificfocus on younger researchers. Some of the topics represented indiscussions will be modular representation theory, coinvariantsand the "hit problem," algebraic topology, and Hasse-Schmidtdifferentials and differential Galois theory.One aspect of invariant theory is studying the question of whatelements of a changing situation must in fact remain fixed. Forexample, the points along the axis of a spinning globe remain inthe same position as the globe turns. The point at the center ofthe spindle of a tape player stays fixed while other points onthe spindle turn around it. More surprisingly, rotating a circlearound its center and then flipping the circle over any linethrough its center must leave a different line in a fixedposition. The search for such "invariant" or "fixed" elements ofa situation can be very subtle, and it arises in a wide varietyof mathematical problems and physical applications. The goal ofthe Ingo2003 conference is to allow mathematicians from differingmathematical disciplines to learn techniques from each other, andto disseminate sets of mathematical tools developed in onediscipline to other disciplines that might find them useful.