I am broadly interested in the relationship between certain groups (such as relatively hyperbolic groups) and geometric properties (such as non-positive curvature and quasi-convexity) of the metrized complexes that they act on.
Currently, I am working on generalizing a result about locally isometric immersions into non-positively curved spaces to the theory of complexes of groups. A complex of groups may be thought of as a set of data describing an action on a polyhedral complex. In that sense, it is a generalization of covering theory.
I am also interested in studying the actions of relatively hyperbolic groups on CAT(0) cube complexes. At the moment, I am interested in structural results related to relative quasi-convexity in the Sageev construction.
Locally Convex Immersions of Complexes of Groups. In preparation.
Relative Quasi-Convexity in the Sageev Construction, 2025 AWM Research Symposium, Special Session on Group, Geometry and Dynamics, University of Wisconsin-Madison