Research Interests
My primary research areas are in geometric group theory and low-dimensional topology. In particular, I am interested in quasi-isometry classification, commensurability classification, and geometric relationship between a group and its subgroups. Most of my research focuses on CAT(0) spaces, relatively hyperbolic groups, right-angled Artin groups, right-angled Coxeter groups, and groups acting on manifolds.
Preprints/submitted papers
1. Superexponential Dehn functions inside CAT(0) groups, (with Noel Brady). SubmittedarXiv:2102.13572.
2. Divergence of finitely presented subgroups of CAT(0) groups, (with Noel Brady). SubmittedarXiv:2012.15803.
3. Coarse Alexander duality for pairs and applications, (with Christopher Hruska and Emily Stark). SubmittedarXiv:2011.00059.
4. The local-to-global property for Morse quasi-geodesics, (with Jacob Russell and Davide Spriano). SubmittedarXiv:1908.11292.
5. Convexity in hierarchically hyperbolic spaces, (with Jacob Russell and Davide Spriano). SubmittedarXiv:1809.09303.
6. Malnormality and join-free subgroups in right-angled Coxeter groups. SubmittedarXiv:1703.09032.
Published/accepted papers
1. Divergence of finitely presented groups, (with Noel Brady). To appear in Groups, Geometry, and DynamicsarXiv:2002.03653.
2. Quasiconvexity in 3-manifold groups, (with Hoang Thanh Nguyen and Wenyuan Yang). To appear in Mathematische AnnalenarXiv:1911.07807.
3. On the coarse geometry of certain right-angled Coxeter groups, (with Hoang Thanh Nguyen). Algebraic and Geometric Topology, 19(6):3075-3118, 2019, arXiv:1712.01079.
4. The relative hyperbolicity and manifold structure of certain right-angled Coxeter groups, (with Matthew Haulmark and Hoang Thanh Nguyen). Internat. J. Algebra Comput., 30(3):501-537, 2020, arXiv:1708.07818.
5. On strongly quasiconvex subgroups. Geometry and Topology, 23(3):1173–1235, 2019, arXiv:1707.05581.
6. Surface group amalgams that (don’t) act on 3-manifolds, (with Christopher Hruska and Emily Stark). American Journal of Mathematics, 142(3):885-921, 2020, arXiv:1705.01361.
7. Divergence spectra and Morse boundaries of relatively hyperbolic groups. Geometriae Dedicata, 194:99–129, 2018., arXiv:1611.05005.
8. On distortion of normal subgroups. To appear in Geometriae Dedicata, arXiv:1611.07453.
9. Geometric embedding properties of Bestvina-Brady subgroups. Algebraic and Geometric Topology, 17(4):2499–2510, 2017., arXiv:1606.00539.
10. Divergence of Morse geodesics. Geometriae Dedicata, 180:385–397, 2016., arXiv:1408.6089.
11. Relative divergence of finitely generated groups. Algebraic and Geometric Topology, 15(3):1717–1769, 2015., arXiv:1406.4232.
12. Relations between various boundaries of relatively hyperbolic groups. Internat. J. Algebra Comput., 23(7):1551–1572, 2013., arXiv:1212.2688.