EMSW21-RTG: Unified Approach to Training in Geometry

摘要奖：DMS-0636557主要研究者：丹尼尔S.作者：Sean M. Keel，Lorenzo A.作者：Karen K. Uhlenbeck UT几何组研究培训补助金是一个垂直整合的计划，以加强本科生，研究生和博士后助理在德克萨斯大学的培训，并通过在网络上发布，超越。 该小组的九名教师将在各个层面开展新的活动。 其中包括一个新的杰出的系列讲座，在几何的观点，这将被广泛传播。 UT的几何组长期以来一直对该领域采取统一的观点。 我们的研讨会反映了我们的方法：他们包括从代数几何，微分几何，全球线性和非线性分析，表示论和拓扑的思想健康的组合。 理论物理学中的概念和灵感通常也会起到一定的作用。 RTG的培训活动旨在向年轻的数学家推广这种几何观，更广泛地说，推广这种数学和科学观。数学是对数字和空间的研究，是科学和技术的基础。 几何学是研究空间的一门学科，它与现实世界有着长期的联系和应用。 在古代世界，测量被引入以促进商业;更先进的概念，如三角学，被引入以了解星星。 在我们的现代世界先进的思想几何基础抽象的物理理论，也有更直接的practicalimplications，例如在编码理论，计算机图形学等有效的培训下一代的几何是至关重要的继续发展这一领域，无论是在inmathematics和外部应用。 德克萨斯大学几何组研究培训补助金（RTG）促进了该领域的统一观点。 通过在奥斯汀的当地活动，并通过网络传播，培训小组将加强各级培训。

AbstractAward: DMS-0636557Principal Investigator: Daniel S. Freed, Sean M. Keel,Lorenzo A. Sadun, Karen K. UhlenbeckThe UT Geometry Group Research Training Grant is a verticallyintegrated program to enhance the training of undergraduates,graduate students, and postdoctoral associates at the Universityof Texas and, through publication on the web, beyond. The ninefaculty members of the Group will initiate new activities at alllevels. Included is a new distinguished lecture series,Perspectives in Geometry, which will be widely disseminated. TheGeometry Group at UT has long taken a unified perspective on thefield. Our seminars reflect our approach: they include a healthymix of ideas from algebraic geometry, differential geometry,global linear and nonlinear analysis, representation theory, andtopology. Often concepts and inspiration from theoreticalphysics play a role as well. The RTG training activities aredesigned to promote this view of geometry and, more broadly, ofmathematics and science to young mathematicians.Mathematics, the study of Number and Space, lies at thefoundation of science and technology. Geometry, the study ofSpace, has long had connections with and applications to the realworld. In the ancient world measurement was introduced tofacilitate commerce; more advanced concepts, such astrigonometry, were introduced to understand the stars. In ourmodern world advanced ideas in Geometry underlie abstracttheories in physics and also have more immediate practicalimplications, for example in coding theory, computer graphics,etc. Effective training of the next generation of Geometers isvital for the continued development of this field, both withinmathematics and for external applications. The University ofTexas Geometry Group Research Training Grant (RTG) promotes aunified view of the field. Through local activities in Austin,and via dissemination on the web, the RTG will enhance trainingat all levels.