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SEMINARS |
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In the first half of the course we will define coarse geometry as an approach to the study of spaces from a "large-scale" perspective, in which two spaces that look the same from a large distance are actually equivalent. The plan is to show that many geometric properties of metric spaces are determined by their large-scale coarse structure. In the middle of the course, we will study some of the coarse invariants of spaces and the useful constructions associated with them. Namely, the ends of metric space and the resulting Freudenthal compactification will be studied. At the end of the course it is planned to give definitions of notions of growth and amenability of rough spaces. This will allow one to consider the apparatus of rough homological algebra. A coarse version of the fixed point theorem will also be considered. The course is designed for undergraduate and graduate students. Prerequisites: group theory, algebraic topology, and functional analysis. Category theory is also desirable. RSS: Forthcoming seminars
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