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

摘要奖：DMS-0309788首席研究员：Kathryn Lesh该奖项将提供资金，以部分支付美国的旅行费用- 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（Ingo 2003）上，来自德国的数学家们发表了他们的论文。起源于17世纪的不变论，已经被证明是数学奋进的一个强有力的领域。 在过去的50年里，它在代数拓扑学、表示论、代数几何以及数论和交换代数等传统领域都有了新的应用。 Lesh教授是Ingo 2003的科学组织委员会成员，Ingo 2003是阿伯丁、曼彻斯特和哥廷根的研究小组在代数拓扑、表示论和交换代数领域的一项倡议。这些科学家发现，跨越狭窄的专业界限的交流可以带来巨大的科学效益。会议的一个中心主题将是不变理论与其他领域的许多联系。在过去，围绕不变量理论的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，或强调与其他学科领域的互动，如代数拓扑。Ingo 2003的组织具有更广泛的科学基础，将是全球意义上的跨学科，并特别关注年轻的研究人员。在讨论中的一些主题将是模块化表示理论，coinvariantsand的“命中问题”，代数拓扑，和Hasse-Schmidtdifferentials和微分伽罗瓦theorety.One方面的不变理论是研究的问题，一个不断变化的情况下，要素实际上必须保持固定。例如，当地球仪转动时，沿着旋转的地球仪的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，而主轴上的其他点绕着它旋转。更令人惊讶的是，绕着它的中心旋转一个圆，然后将圆翻转到通过它的中心的任何一条线上，一定会在固定的位置留下一条不同的线。 寻找这种“不变的”或“固定的”元素的情况可以是非常微妙的，它出现在各种各样的数学问题和物理应用。Ingo 2003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，并将一个学科开发的数学工具集传播给可能发现它们有用的其他学科。

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.