Travel Funding for Workshop at RIMS Kyoto

近年来，在与所谓的Grothendieck Anabelian程序相关的数学领域有一个非常密集的研究活动，其中一些突出的开放问题是算术几何中的截面猜想及其蕴含，通过(几何)基本群上的算术作用来描述数域的伽罗瓦结构，以及前定Teichmueller理论及其与算术和数论的关系。当然，这一数学领域的主要努力之一是在代数和数论的背景下理解Grothendieck的Anabelian程序的更大图景。2009年7月至12月，在英国剑桥的艾萨克·牛顿研究所，为期半年的NAG计划致力于解决这一问题，并被证明是一项非常成功的活动。通过目前的会议资金提案，PI促进了美国科学家(研究生和初级/高级研究人员)于2010年10月20日至30日在日本京都参加一个分为两部分的数学研究活动，这可以被视为NAG计划的延续。《京都议定书》活动的绝大多数参与者来自欧洲和日本。活动的第一部分是介绍性的，将为研究生和年轻研究人员举办几次讲座和特别活动，从而加强培训和对技术的了解，而活动的第二部分将两者兼而有之：首先，通过各自相关研究领域的世界领先专家的一系列调查演讲，展示Grothendieck Anabelian计划的广泛现状。第二，让初级和资深科学家有机会展示他们在这一研究领域的最新发现和想法。因此，该活动将有助于为各级的国际合作、培训和科学交流创造一个广泛的基础。这项活动的结果将通过互联网和日本数学学会将出版的会议论文集向数学界传播。

In recent years there is a very intensive research activity in areas of Mathematics related to the so called Grothendieck's anabelian program, where some of the outstanding open problems are the section conjecture and its implications in arithmetic geometry, the description of the Galois structure of number fields via the arithmetic action on (geometric) fundamental groups, and the profinite Teichmueller theory and its relation to Arithmetic and Number Theory. Naturally, one of the major effort in this area of mathematics is to understand the bigger picture of Grothendieck's anabelian program in the context of Algebra and Number Theory. The half year long NAG Programme at the Isaac Newton Institute in Cambridge, UK, in July-December 2009, was dedicated to this circle of questions and turned out to be a very successful activity.Through the present conference funding Proposal, the PI facilitates the participation of American scientists (grad students and junior/senior researchers) to a two part mathematical research activity in Kyoto, Japan, during October 20-30, 2010, which could be viewed as a continuation of the NAG Programme. The wide majority of the participants to the Kyoto activity come from Europe and Japan. The first part of the activity is of introductory nature and will host several talks and special activities for graduate students and young researchers, thus enhancing training and technological understanding, whereas the second part of the activity will do both: First, present of wide picture of the state of the art of Grothendieck's anabelian program through a series of survey talks by world leading experts in respective related areas of research. Second, give junior and senior scientists the opportunity to present their newest findings and ideas in this area of research. Thus the activity will contribute to creating a broad basis for international cooperation, training, and scientific exchange at all levels. The outcomes of the activity will be disseminated to the mathematical community via the Internet and a proceedings volume to be published by the Mathematical Society of Japan.