SGER: Midwest Topology Network

中西部包含一个大型网络的积极研究人员在代数拓扑分布通过几十所大学和学院。 定期会议不断激发新的想法和潜在的新研究方向。 这项补助金的目的是提供手段，以促进新的合作和新的研究项目之间的中西部拓扑学家在不同的大学，否则将无法进行。 该补助金将支持三种主要类型的活动：研究合作旅行，初学者的旅行，以及与其他网络的交流。代数拓扑试图将空间和几何问题简化为代数问题。 这通常涉及将某种代数对象（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。 这种自由常常允许拓扑学家将复杂的问题变形为具有相同不变量的更简单的问题，从而更容易计算。 由于较简单的问题往往保留了关于原始数学对象的重要信息，代数拓扑为广泛的数学问题提供了有效的工具。

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.