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Asymptotic Cones

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If you have a question about this talk, please contact Alexis Marchand.

The Asymptotic Cone of a metric space X is a space that represents how X looks if we look at it from “infinitely far”. More precisely, it is the ultralimit of a sequence of rescaled copies of X. We will begin by giving the definition of an asymptotic cone. We will then discuss how asymptotic cones of groups (equipped with the word metric) relate to various geometric and algebraic properties of the group. Little or no advance knowledge is assumed on the part of the audience (very much in spirit of the seminar!).

This talk is part of the Junior Geometry Seminar series.

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