Research area: geometric group theory
My research interests lie in graphs and metric spaces satisfying various nonpositive curvature-like conditions and on groups acting on such graphs and spaces. This is an area of study that traces its origins to the work of Max Dehn on fundamental groups of surfaces in the early 20th century and that includes the development of small cancellation groups, CAT(0) groups, hyperbolic groups, cubulated groups, systolic groups, hierarchically hyperbolic groups, coarse median groups and, most recently, Helly groups. In all of these families of groups, particular nonpositive curvature conditions can be exploited to find interactions between the geometry and the algebraic properties of the groups. My own research is focused primarily on the study of strongly shortcut groups, Helly groups, hierarchically hyperbolic groups and quadric groups.
T. Haettel, N. Hoda, H. Petyt, The coarse Helly property, hierarchical hyperbolicity, and semihyperbolicity, Geom. Topol., to appear, 35 pages.
N. Hoda, Shortcut Graphs and Groups, Trans. Am. Math. Soc. 375 (2022), no. 4, 2417–2458.
N. Hoda, Quadric Complexes, Mich. Math. J. 69 (2020), no. 2, 241–271.