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Tuesday, January 24, 2017

**Abstract:** There are natural embeddings of right-angled Artin groups $G$ into the mapping class group $Mod(S)$ of a surface $S$. The groups $G$ and $Mod(S)$ can each be equipped with a geometric structure called a hierarchically hyperbolic space (HHS) structure, and there is a notion of a boundary for such spaces. In this talk, we will explore the following question: does an embedding $\phi: G \rightarrow Mod(S)$ extend continuously to a boundary map $\partial G \rightarrow \partial Mod(S)$? That is, given two sequences $(g_n)$ and $(h_n)$ in $G$ that limit to the same point in $\partial G$, do $(\phi(g_n))$ and $(\phi(h_n))$ limit to the same point in $\partial Mod(S)$? No background in HHS structures is needed.