61 citations · 175 across the 11 of their papers we have counts for
11 papers
Cubulating Infinity in Hierarchically Hyperbolic Spaces
Matthew Gentry Durham
We prove that the hierarchical hull of any finite set of interior points, hierarchy rays, and boundary points in a hierarchically hyperbolic space (HHS) is quasi-median quasi-isome…
The geometry of genericity in mapping class groups and Teichmüller spaces via CAT(0) cube complexes
Matthew Gentry Durham, Abdul Zalloum
Random walks on spaces with hyperbolic properties tend to sublinearly track geodesic rays which point in certain hyperbolic-like directions. Qing-Rafi-Tiozzo recently introduced th…
Extensions of Veech groups II: Hierarchical hyperbolicity and quasi-isometric rigidity
Spencer Dowdall, Matthew G. Durham, Christopher J. Leininger +1
We show that for any lattice Veech group in the mapping class group of a closed surface , the associated --extension group is a hierarchically hyperboli…
Stable cubulations, bicombings, and barycenters
Matthew G. Durham, Yair N. Minsky, Alessandro Sisto
We prove that the hierarchical hulls of finite sets of points in mapping class groups and Teichmüller spaces are stably approximated by a CAT(0) cube complexes, strengthening a res…
Extensions of Veech groups I: A hyperbolic action
Spencer Dowdall, Matthew G. Durham, Christopher J. Leininger +1
Given a lattice Veech group in the mapping class group of a closed surface , this paper investigates the geometry of , the associated --extension group. We prove that $…
Graphs of curves on infinite-type surfaces with mapping class group actions
Matthew Gentry Durham, Federica Fanoni, Nicholas G. Vlamis
We study when the mapping class group of an infinite-type surface admits an action with unbounded orbits on a connected graph whose vertices are simple closed curves on . We…
Pulling back stability with applications to Out() and relatively hyperbolic groups
Tarik Aougab, Matthew Gentry Durham, Samuel J. Taylor
We prove that stability -- a strong quasiconvexity property -- pulls back under proper actions on proper metric spaces. This result has several applications, including that convex…
Boundary convex cocompactness and stability of subgroups of finitely generated groups
Matthew Cordes, Matthew Gentry Durham
A Kleinian group is called convex cocompact if any orbit of in is quasiconvex or, equivalently, acts cocompactly on the convex…
Boundaries and automorphisms of hierarchically hyperbolic spaces
Matthew G. Durham, Mark F. Hagen, Alessandro Sisto
Hierarchically hyperbolic spaces provide a common framework for studying mapping class groups of finite type surfaces, Teichmüller space, right-angled Artin groups, and many other…
The asymptotic geometry of the Teichmüller metric: Dimension and rank
Matthew Gentry Durham
We analyze the asymptotic cones of Teichmüller space with the Teichmüller metric, . We give a new proof of a theorem of Eskin-Masur-Rafi which bounds the dime…
Convex cocompactness and stability in mapping class groups
Matthew Gentry Durham, Samuel J. Taylor
We introduce a strong notion of quasiconvexity in finitely generated groups, which we call stability. Stability agrees with quasiconvexity in hyperbolic groups and is preserved und…