SGER: Midwest Topology Network

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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.