EMSW21-RTG: Unified Approach to Training in Geometry

奖：DMS-0636557主要研究员：Daniel S.Freed，Sean M.Keel，Lorenzo A.Sadun，Karen K.Uhlenbeck德克萨斯大学几何小组研究培训助学金是一个垂直整合的计划，旨在加强德克萨斯大学本科生、研究生和博士后助理的培训，并通过在网上发布，超越。该小组的九名教职员工将在所有级别发起新的活动。包括一个新的著名系列讲座，几何透视，这将被广泛传播。德克萨斯大学的几何小组长期以来对这一领域采取了统一的观点。我们的研讨会反映了我们的方法：它们包括来自代数几何、微分几何、全局线性和非线性分析、表示理论和拓扑学的思想的健康混合。通常，来自理论物理学的概念和灵感也起到了作用。RTG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，是对数学和科学的看法。数学是研究数字和空间的学科，是科学和技术的基础。几何学是一门研究空间的学科，长期以来一直与现实世界联系在一起，并应用于现实世界。在古代，测量被引入以促进商业；更先进的概念，如天文计量学，被引入以了解恒星。在我们的现代世界中，几何中的先进思想是物理抽象理论的基础，也具有更直接的实际意义，例如在编码理论、计算机图形学等方面。有效地培训下一代几何学家对于这一领域的持续发展至关重要，无论是在数学领域还是在外部应用。德克萨斯大学几何小组研究培训基金(RTG)促进了对该领域的统一看法。通过在奥斯汀的当地活动和在网上传播，技术小组将加强各级的培训。

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.