Research

• "Curtain Characterization of Sublinearly Morse Geodesics in CAT(0) Spaces". September 2023. Arxiv Preprint

-- Abstract: We show that the sublinear Morse boundary of every CAT(0) space continuously injects into the Gromov boundary of a hyperbolic space, which was not previously known even for all CAT(0) cube complexes. Our work utilizes the curtain machinery introduced by Petyt-Spriano-Zalloum. Curtains are more general combinatorial analogues of hyperplanes in cube complexes, and we develop multiple curtain characterizations of the sublinear Morse property along the way. Our results answer multiple questions of Petyt-Spriano-Zalloum. 

• "The Curtain Model is Not a Quasi-Isometry Invariant of CAT(0) Spaces."  December 2023. Arxiv Preprint

-- Abstract:  Petyt-Spriano-Zalloum recently developed the notion of a curtain model, which is a hyperbolic space associated to any CAT(0) space.  It plays a similar role for CAT(0) spaces that curve graphs do for mapping class groups of finite-type surfaces.  Those authors asked whether this curtain model is a quasi-isometry invariant, namely if quasi-isometric CAT(0) spaces have quasi-isometric curtain models.  In this short note, we provide an explicit example answering this question in the negative.

• "Geometry and Dynamics on Sublinearly Morse Boundaries of Proper Geodesic Groups”. (In preparation with Yulan Qing and Jacob Garcia)