The Large-Scale Geometry of Groups, and Spaces with Nonpositive Curvature. More specifically, the investigator is interested in relations between a discrete group and the large scale structure of its Cayley graphs, and applications of these to geometric and dynamical problems involving negatively curved surfaces. . In mathematics as well as in physics and chemistry, groups are often used to describe various symmetry properties.
Discrete groups are finite, hence, objects that can be written down rather explicitly.
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