Colloquium | Tianyi Zheng (UC San Diego)

Title: Contractions in self-similar groups

Abstract: In this talk we discuss groups acting on rooted trees, or more generally on a Cantor set, with self-similarity. Since the first construction of groups of intermediate growth due to Grigorchuk, length contractions under recursions have been studied. Such contractions are closely related to volume growth, amenability, and other properties of the group. We will explain various measurements of complexity and connections to the conformal dimension of the associated limit space. Based on joint works with Bartholdi, Matte Bon, and Nekrashevych.

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