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RESEARCH

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Research Interests

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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 relationships 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.

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Preprints/submitted papers

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1. Superexponential Dehn functions inside CAT(0) groups, (with Noel Brady). Submitted, arXiv:2102.13572.

 

2. Coarse Alexander duality for pairs and applications, (with Christopher Hruska and Emily Stark). Submitted, arXiv:2011.00059.​

 

3. Malnormality and join-free subgroups in right-angled Coxeter groups. Submitted, arXiv:1703.09032.

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Published/accepted papers

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1. The local-to-global property for Morse quasi-geodesics, (with Jacob Russell and Davide Spriano). To appear in Mathematische Zeitschrift, arXiv:1908.11292.

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2. Divergence of finitely presented subgroups of CAT(0) groups, (with Noel Brady). To appear in Pacific Journal of Mathematics, arXiv:2012.15803.

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3. Divergence of finitely presented groups, (with Noel Brady). To appear in Groups, Geometry, and Dynamics, arXiv:2002.03653.

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4. Quasiconvexity in 3-manifold groups, (with Hoang Thanh Nguyen and Wenyuan Yang). To appear in Mathematische Annalen, arXiv:1911.07807.

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5. Convexity in hierarchically hyperbolic spaces, (with Jacob Russell and Davide Spriano). To appear in Algebraic and Geometric Topology, arXiv:1809.09303.

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6. 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.

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7. 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.

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8. On strongly quasiconvex subgroups. Geometry and Topology, 23(3):1173–1235, 2019, arXiv:1707.05581.

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9. 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.

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10. Divergence spectra and Morse boundaries of relatively hyperbolic groups. Geometriae Dedicata, 194:99–129, 2018., arXiv:1611.05005.

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11. On distortion of normal subgroups. Geometriae Dedicata, 212:261-279, 2021., arXiv:1611.07453.

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12. Geometric embedding properties of Bestvina-Brady subgroups. Algebraic and Geometric Topology, 17(4):2499–2510, 2017., arXiv:1606.00539.

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13. Divergence of Morse geodesics. Geometriae Dedicata, 180:385–397, 2016., arXiv:1408.6089.

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14. Relative divergence of finitely generated groups. Algebraic and Geometric Topology, 15(3):1717–1769, 2015., arXiv:1406.4232.

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15. Relations between various boundaries of relatively hyperbolic groups. Internat. J. Algebra Comput., 23(7):1551–1572, 2013., arXiv:1212.2688.

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