Writings

Published Papers:

1. Algorithmic detection and description of hyperbolic structures on closed 3-manifolds with solvable word problem. Geom. Topol. 6 (2002), 1–25. 

2. Geometry of pseudocharacters. Geom. Topol. 9 (2005), 1147–1185. 

3. Quasi-actions on trees and property (QFA).  With an appendix by N. Monod and B. Rémy. J. London Math. Soc. (2) 73 (2006), no. 1, 84–108. 

4. Fillings, finite generation and direct limits of relatively hyperbolic groups, with D. Groves. Groups Geom. Dyn. 1 (2007), no. 3, 329–342. 

5. Actions of certain arithmetic groups on Gromov hyperbolic spaces. Algebr. Geom. Topol. 8 (2008), no. 3, 1371–1402.

6. Dehn filling in relatively hyperbolic groups, with D. Groves. Israel J. Math. 168 (2008), 317–429.

7. Residual finiteness, QCERF and fillings of hyperbolic groups, with I. Agol and D. Groves. Geom. Topol. 13 (2009), no. 2, 1043–1073. 

8. Separation of relatively quasiconvex subgroups, with E. Martínez-Pedroza. Pacific J. Math. 244 (2010), no. 2, 309–334. 

9. Virtually geometric words and Whitehead's algorithm. Math. Res. Lett. 17 (2010), no. 5, 917–925. 

10. CAT(0) and CAT(−1) fillings of hyperbolic manifolds, with K. Fujiwara. J. Differential Geom. 85 (2010), no. 2, 229–269.

11. Simplicial volume and fillings of hyperbolic manifolds, with K. Fujiwara. Algebr. Geom. Topol. 11 (2011), no. 4, 2237–2264.

12. Filling virtually special subgroups, with I. Agol and D. Groves.  Appendix to "The virtual Haken conjecture" by Ian Agol. Documenta Mathematica 18 (2013) pp. 1045–1087

13. Virtual geometricity is rare, with C. Cashen. LMS J. Comput. Math. 18 (2015), no. 1, 444–455. 

14. Non-faithful representations of surface groups into SL(2,C) which kill no simple closed curve, with D. Cooper. Geom. Dedicata 177 (2015), 165–187. 

15. An alternate proof of Wise's malnormal special quotient theorem, with I. Agol and D. Groves. Forum Math. Pi 4 (2016), e1, 54 pp. 

16. Dehn fillings and elementary splittings, with D. Groves. Trans. Amer. Math. Soc. 370 (2018), no. 5, 3017–3051. 

17. Generalized triangle groups, expanders, and a problem of Agol and Wise, with A. Lubotzky and H. Wilton. Comment. Math. Helv. 94 (2019), no. 1, 53–66. 

18. Boundaries of Dehn fillings, with D. Groves and A. Sisto. Geom. Topol. 23 (2019), no. 6, 2929–3002.

19. Cohomology and the Bowditch boundary, with O. Wang. Michigan Math. J. 69 (2020), no. 3, 633–669.

20. Quasiconvexity and Dehn filling, with D. Groves. Amer. J. Math. 143 (2021), no. 1, 95–124.

21. Specializing cubulated relatively hyperbolic groups, with D. Groves. J. Topol. 15 (2022), no. 2, 398–442.

22. Special IMM groups, with D. Groves. Bull. Lond. Math. Soc. 55 (2023), no. 2, 717–722. 

23. Stability for hyperbolic groups acting on boundary spheres, with K. Mann. Forum Math. Sigma 11 (2023), Paper No. e83, 25 pp.

24. Hyperbolic groups acting improperly, with D. Groves. Geom. Topol. 27 (2023), no. 9, 3387–3460.

25. Acylindrically hyperbolic groups and their quasi-isometrically embedded subgroups, with C. Abbott. Michigan Math. J. 74 (2024), no. 2, 357–402.

26. Tracks and cubulations, with M. Mj and M. Sageev.  Appendix to "Cubulating surface-by-free groups," by M. Mj. J. Topol. 17 (2024), no. 4, e70011, 65 pp.

27. A criterion for residual finiteness, with D. Groves.  Appendix to "Relative cubulation of relative strict hyperbolization," by J.-F. Lafont and L. Ruffoni.  J. Lond. Math. Soc. (2) 111 (2025), no. 4, e70093, 30pp.

28. Stability of hyperbolic groups acting on their boundaries, with K. Mann and T. Weisman. Groups Geom. Dyn. (2025), published online, awaiting issue placement.

29. Topological stability of relatively hyperbolic groups acting on their boundaries, with K. Mann and T. Weisman.  Math. Z. 312, 5 (2026). 

Preprints:

1. Recognizing geometric 3-manifold groups using the word problem, with D. Groves and H. Wilton. arXiv:1210.2101.

2. The Bowditch boundary of (G,H) when G is hyperbolic. arXiv:1504.03630.

3. Drilling hyperbolic groups, with D. Groves, P. Haïssinsky, D. Osajda, A. Sisto, and G.S. Walsh.  arXiv:2406.14667

4. Pseudo-Anosov surfaces and Dynamics in 3-manifolds, with C. Neofytidis. arXiv:2503.02873

5. Coning off totally geodesic boundary components of a hyperbolic manifold, with C Kelln.  arXiv:2504.21652

My current research is supported by the Simons Foundation, under Collaboration Grant 942496.