Temple University 3 credits MATH
This course surveys the rapidly expanding field of geometric group theory, focusing on the role played by negative curvature. The course begins with classical combinatorial techniques used to construct and study infinite discrete groups. After introducing basic concepts in coarse geometry, it turns attention to Gromov's notion of hyperbolic groups. In addition to studying geometric, algebraic, and algorithmic properties of these groups, the course keeps an eye towards several generalizations of hyperbolicity that have recently played a large role in understanding many geometrically significant groups. As examples, it also touches on the study of mapping class groups, outer automorphism groups of free groups, and cubical groups.
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