Groups and Dynamics Seminar

Date: December 2, 2020

Time: 12:00PM - 1:00PM

Location: online

Speaker: Wenhao Wang, Vanderbilt University

Title: Dehn Functions of Finitely Presented Metabelian Groups

Abstract: The Dehn function was introduced by computer scientists Madlener and Otto to describe the complexity of the word problem of a group, and also by Gromov as a geometric invariant of finitely presented groups. In this talk, I will show that the upper bound of the Dehn function of finitely presented metabelian group $G$ is $2^\{n^\{2k\}\}$, where $k$ is the minimal torsion-free rank of abelian group T such that there exists an abelian group $A$ satisfying $G/A \cong T$, answering the question that if the Dehn functions of metabelian groups are uniformly bounded. I will also talk about the relative Dehn function of finitely generated metabelian group and its relation to the Dehn function.