Workshops in Geometric Topology

这笔赠款将用于资助将于2015年6月25日至27日在德克萨斯州沃斯堡的德克萨斯基督教大学举办的第32届几何拓扑学年度研讨会，以及将于2016年和2017年由科罗拉多学院和杨百翰大学主办的第33届和第34届研讨会。这样的数学研讨会为在某个子领域工作的数学家提供了一个机会，在这种情况下是几何拓扑学，通过正式的演讲和非正式的讨论来见面、互动和分享他们的研究。补助金将主要用于支持与会者的旅费和出席费用，特别是研究生、年轻博士和其他没有自己资金来源的研究人员。广义地说，几何拓扑学是研究物理宇宙中的空间形态和可以模拟现实生活现象的抽象“空间”。例如，拓扑学家可能会研究物理弦或蛋白质链在真实的三维世界中是如何打结的，或者他或她可能会研究机器可能居住的抽象位置空间，从而允许任意数量的参数来描述各种组件的位置。这一领域的研究可以从高度抽象到由这些抽象基础支持的更具体的应用。拓扑学的现代应用涉及机器人运动规划、数据分析、图像处理、传感器网络和数学生物学等多个领域。几何拓扑学研讨会的一个主要目标是为几何拓扑学(以及最近与几何群论密切相关的领域)的数学家提供一个与该领域其他人讨论工作的机会。另一个重要目标是让一位国家公认的专家讨论当前感兴趣的一个重要领域，从而扩大参与者的利益。第三个目标是提供一个严肃但非正式的研究氛围，让研究生可以在其中认识并向该领域的其他人学习。在每个研讨会上，参与者将有机会参加由一位主要演讲者所作的三次讲座，这位演讲者是根据他或她的顶级研究资历和高超的解释能力而被选中的。第32届年度研讨会的主要演讲者将是国际知名的波恩大学和豪斯多夫数学研究所的沃尔夫冈·Lück；他将介绍L2-Betti数和法雷尔-琼斯猜想，然后介绍三维流形的应用。其他研讨会参与者将被邀请在融洽的环境中通过简短的演讲分享他们的工作，并将为参与者之间和主要发言者之间的非正式讨论和互动提供重要的时间。总体而言，研讨会将为几何拓扑学家提供互动和分享想法的机会，从而导致可能的研究合作。研讨会将在全国范围内进行广告宣传。研究生和代表不足群体的成员将获得最优先的资助，并将特别鼓励他们参加会议和发言。第32届年度研讨会的网址为：http://faculty.tcu.edu/gfriedman/GTW2015/

This grant is to fund the 32nd annual Workshop in Geometric Topology, to be hosted at Texas Christian University in Fort Worth, Texas, June 25-27, 2015, as well as the 33rd and 34th workshops in 2016 and 2017, to be hosted by Colorado College and Brigham Young University. Such mathematics workshops provide an opportunity for mathematicians working in a certain subfield, in this case geometric topology, to meet, interact, and share their research through both official lecture presentations and informal discussions. Grant funds will be utilized primarily to support the travel and attendance costs of conference participants, particularly graduate students, young Ph.D.s, and other researchers without their own sources of funding.The field of geometric topology, broadly speaking, is the study of spatial configuration, both in the physical universe and of abstract "spaces" that can model real-life phenomena. For example, a topologist might study how a physical string or protein strand is knotted in the real three-dimensional world, or he or she might study the abstract space of positions that a machine could inhabit, allowing for an arbitrary number of parameters that describe the positions of various components. Research in this field can vary from the highly abstract to more concrete applications supported by those abstract underpinnings. Modern applications of topology occur in such diverse areas as robot motion planning, data analysis, image processing, sensor networks, and mathematical biology.A primary goal of these Workshops in Geometric Topology is to provide mathematicians in geometric topology (and, more recently, the closely related field of geometric group theory) who have active research programs, but limited support, an opportunity to discuss their work with others in the field. Another important goal is to expand the interests of the participants by having a nationally-recognized expert discuss an important area of current interest. A third goal is to provide a serious but informal research atmosphere in which graduate students can meet and learn from others in the field. At each workshop, participants will have the opportunity to attend three lectures given by a principal speakers chosen for his or her top-tier research credentials and superb expository abilities. The principal speaker at the 32nd annual Workshop will be the internationally-renowned Wolfgang Lück of the University of Bonn and the Hausdorff Research Institute for Mathematics; he will provide introductory talks about L2-Betti numbers and the Farrell-Jones Conjecture and then a talk about applications to 3-manifolds. The other workshop participants will be invited to share their own work by giving short talks in a congenial environment, and important time will be provided for informal discussion and interaction among participants and with the principal speaker. Overall, the workshops will provide opportunities for geometric topologists to interact and share ideas, leading to possible research collaborations. The workshops will be advertised nationally. Graduate students and members of underrepresented groups will be given top priority for funding and will be particularly encouraged to attend and to speak. The website for the 32nd annual workshop can be found at http://faculty.tcu.edu/gfriedman/GTW2015/