SGER: Midwest Topology Network

SGER：中西部拓扑网络

• 批准号: 0844249
• 负责人: Michael Mandell
• 金额: $ 20万
• 依托单位: Indiana University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2008
• 资助国家: 美国
• 起止时间: 2008-09-01 至 2011-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0844249&HistoricalAwards=false
• 关键词: SGER; Midwest; Topology; Network

The midwest contains a large network of active researchers in algebraic topology spread out through dozens of universities and colleges. Regular conferences continually spark new ideas and potential new research directions. The purpose of this grant is to provide the means to foster the new collaborations and new research projects among midwest topologists at different universities that would otherwise go unpursued. This grant would support three key types of activity: Travel for research collaboration, travel for beginning researchers, and exchange with other networks.Algebraic topology attempts to reduce questions about space and geometry to questions in algebra. Often this involves assigning some kind of algebraic object like a vector space or numerical invariant to a geometric object or space to capture or measure some intrinsic feature. These invariants can then potentially be used to distinguish between different spaces. The invariants studied are typically discrete, and so they do not change under continuous deformation or "homotopy". This freedom often allows topologists to deform complicated problems into simpler ones that have the same invariants, which are then easier to compute. Since the simpler problems often retain important information about the original mathematical objects, algebraic topology provides effective tools for a wide range of mathematical problems.

中西部拥有一个庞大的代数拓扑研究人员网络，遍布数十所大学和学院。 定期会议不断激发新想法和潜在的新研究方向。 这笔赠款的目的是提供手段，促进中西部不同大学的拓扑学家之间的新合作和新研究项目，否则这些合作和新研究项目将无法实现。 这笔赠款将支持三种关键类型的活动：研究合作旅行、初级研究人员旅行以及与其他网络的交流。代数拓扑试图将有关空间和几何的问题简化为代数问题。 通常，这涉及将某种代数对象（例如向量空间或数值不变量）分配给几何对象或空间以捕获或测量某些内在特征。 这些不变量可以用来区分不同的空间。 研究的不变量通常是离散的，因此它们在连续变形或“同伦”下不会改变。 这种自由通常允许拓扑学家将复杂的问题转化为具有相同不变量的简单问题，从而更容易计算。 由于较简单的问题通常保留有关原始数学对象的重要信息，因此代数拓扑为广泛的数学问题提供了有效的工具。