EMSW21-RTG: Unified Approach to Training in Geometry

摘要：获奖：dms -0636557首席研究员：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基金是一个垂直整合的项目，旨在加强德克萨斯大学本科生、研究生和博士后的培训，并通过在网络上发布，并在其他地方。该小组的九名教员将在各级开展新的活动。包括一个新的杰出的系列讲座，透视几何，这将广泛传播。德克萨斯大学的几何小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：它们包括代数几何，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组合。通常，来自理论物理学的概念和灵感也发挥了作用。RTG的培训活动旨在向年轻数学家推广这种几何观点，更广泛地说，是对数学和科学的看法。数学是对数和空间的研究，是科学技术的基础。几何学是对空间的研究，长期以来一直与现实世界有联系并应用于现实世界。在古代，计量被引入是为了促进商业；更先进的概念，如天文学，被引入来了解恒星。在我们的现代世界，几何学的先进思想是物理学抽象理论的基础，也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。对下一代几何学家的有效培训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领域。德克萨斯大学几何小组研究培训补助金（RTG）促进了该领域的统一观点。通过奥斯汀当地的活动，并通过网络传播，RTG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.