Workshops in Geometric Topology

几何拓扑研讨会

• 批准号: 1461385
• 负责人: Craig Guilbault
• 金额: $ 5.02万
• 依托单位: University of Wisconsin-Milwaukee
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2015
• 资助国家: 美国
• 起止时间: 2015-06-01 至 2019-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1461385&HistoricalAwards=false
• 关键词: Workshops; Geometric; Topology

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/

这笔赠款是资助第32届几何拓扑年度研讨会，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，以及2016年和2017年的第33和第34届研讨会，由科罗拉多学院和杨百翰大学主办。这样的数学研讨会提供了一个机会，数学家工作在某一子领域，在这种情况下几何拓扑，以满足，互动，并分享他们的研究，通过正式演讲和非正式讨论。 补助金将主要用于支持与会者的差旅费和出席会议的费用，特别是研究生、年轻的博士和其他没有自己资金来源的研究人员。几何拓扑学的领域，广义上说，是空间配置的研究，无论是在物理宇宙中还是抽象的“空间”，可以模拟现实生活中的现象。例如，拓扑学家可能研究物理弦或蛋白质链在真实的三维世界中如何打结，或者他或她可能研究机器可以居住的抽象位置空间，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。拓扑学的现代应用出现在机器人运动规划、数据分析、图像处理、传感器网络和数学生物学等不同领域。这些几何拓扑学研讨会的主要目标是为数学家提供几何拓扑学（以及最近与几何群论密切相关的领域），他们有活跃的研究计划，但支持有限，有机会与该领域的其他人讨论他们的工作。另一个重要的目标是通过让一位国家公认的专家讨论当前感兴趣的一个重要领域来扩大与会者的兴趣。第三个目标是提供一个严肃但非正式的研究氛围，使研究生能够在该领域与他人会面并向他人学习。在每次研讨会上，与会者将有机会参加三个讲座，由一位主要发言人为他或她的顶级研究证书和高超的技能所选择。第32届年度研讨会的主要发言人将是国际知名的波恩大学和豪斯多夫数学研究所的Wolfgang Lück;他将提供关于L2-Betti数和Farrell-Jones猜想的介绍性演讲，然后讨论3-流形的应用。将邀请讲习班其他与会者在气氛融洽的环境中作简短的发言，介绍他们的工作，并将为与会者之间以及与主要发言者进行非正式讨论和互动提供重要时间。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，从而促成可能的研究合作。讲习班将在全国范围内进行宣传。研究生和代表性不足的群体的成员将获得最优先的资助，并将特别鼓励参加和发言。第32届年度研讨会的网址为http://faculty.tcu.edu/gfriedman/GTW2015/