**Seminario Teoría de Grupos ICMAT-UAM **

**Miercoles 4 de Diciembre, 12:30, Aula 520, Modulo 17, Ciencias, UAM **

**Claudio Llosa Isenrich (Max Planck Institute for Mathematics) **

**Title: Lower bounds on Dehn functions of residually free groups **

**Abstract: **

**The Dehn function of a finitely presented group $G$ with finite generating set $X$ is a quantitative measure for the difficulty of detecting whether a word in $X$ represents the trivial element in $G$. Dison raised the question if residually free groups admit a uniform polynomial upper bound on their Dehn functions. It is motivated by the existence of uniform polynomial upper bounds on interesting families of residually free groups, such as the Stallings--Bieri groups. In this talk we will show that the answer to Dison's question is negative, by proving that for every $rgeq 3$ there is a subgroup $G_r$ of a direct product of $r$ free groups with Dehn function bounded below by $n^r$. This is joint work with Romain Tessera. **