Travel Funding for Workshop at RIMS Kyoto

近年来，在与所谓的Grothendieck的anabel纲领有关的数学领域中，有一个非常密集的研究活动，其中一些突出的开放问题是截面猜想及其在算术几何中的含义，通过算术作用描述数域的Galois结构，（几何）基本群，和profinite Teichmueller理论及其关系算术和数论。自然，在这一领域的数学的主要努力之一是了解更大的图片格罗滕迪克的anabelian计划的背景下代数和数论。2009年7月至12月，在英国剑桥的艾萨克·牛顿研究所开展了为期半年的NAG计划，致力于解决这一问题，并取得了非常成功的成果。通过目前的会议资助提案，PI促进了美国科学家的参与（格拉德生和初级/高级研究人员）参加了2010年10月20日至30日在日本京都举行的两部分数学研究活动，这可以被看作是NAG计划的延续。参加京都活动的绝大多数人来自欧洲和日本。活动的第一部分是介绍性的，将为研究生和青年研究人员举办几次讲座和特别活动，从而加强培训和技术理解，而活动的第二部分将做到这两点：第一、通过一系列由世界领先的相关研究领域的专家进行的调查讲座，展示了格罗滕迪克的anabelian计划的最新发展状况。第二，让初级和高级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，这项活动将有助于为各级的国际合作、培训和科学交流奠定广泛的基础。活动的成果将通过互联网和日本数学学会出版的会议记录分发给数学界。

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.