arXiv page

MathSciNet Reviews

Preprints and publications

1. Conjugator length in finitely presented groups
   with Martin Bridson and Andrew Sale. arXiv version

2. Groups with fast-growing conjugator length functions
   with Martin Bridson. arXiv version

3. Snowflake groups and conjugator length functions with non-integer exponents
   with Martin Bridson. arXiv version

4. Distinguishing filling invariants associated to conjugacy in groups
   with Conan Gillis. arXiv version

5. Linear Diophantine equations and conjugator length in 2-step nilpotent groups
   with Martin Bridson, The Bulletin of the London Mathematical Society, 58(e70327), 2026. arXiv version

6. The lengths of conjugators in the model filiform groups
   with Martin Bridson, Mathematische Zeitschrift, Math. Z., 312(97), 2026. arXiv version

7. Conjugacy in a family of free-by-cyclic groups
   with Martin Bridson and Andrew Sale, to appear in the Michigan Mathematical Journal. arXiv version

8. Strong shortcuts, generating sets, and isometric circles in asymptotic cones
   with Nima Hoda, to appear in the Proceedings of the American Mathematical Society. arXiv version

9. Fractional distortion in hyperbolic groups
   with Pallavi Dani, to appear in Advances in Mathematics. arXiv version

10. Active learning taking root—a progress update
    with David Freund, Tara Holm, and Marie MacDonald, PRIMUS, 1–21, 2024. Preprint version

11. Exponentially distorted subgroups in wreath products
    Q. J. Math. Oxford, Volume 75, Issue 4, December 2024, pages 1355—1361. arXiv version

12. Dehn functions of mapping tori of right-angled Artin groups
    with Kristen Pueschel, Glasgow Math. Journal. 2024;66(2):252-289. arXiv version

13. The Generalized Dehn Property does not imply a linear isoperimetric inequality
    with Owen Baker, Ann. Math. Qué. 44 (2020), no. 1, 1–7. arXiv version

14. Soficity and variations on Higman's group
    with Martin Kassabov and Vivian Kuperberg, Journal of Combinatorial Algebra, 3(1), pages 41–70, 2019. arXiv version

15. Computing area in presentations of the trivial group
    Proc. Amer. Math. Soc. 145 (2017), 5059–5069. arXiv version

16. Taming the hydra: the word problem and extreme integer compression
    with Will Dison and Eduard Einstein, Internat. J. Algebra Comput., 28(07), pages 1299–1381, 2018. arXiv version. 

Extended abstract: Ackermannian integer compression and the word problem for hydra groups, Mathematical Foundations of Computer Science 2016 (Krakow) 

17. Lamplighters, metabelian groups, and horocyclic products of trees
    with Margarita Amchislavska, L'Enseignement Mathématique, 61, pages 373–415, 2015. arXiv version

18. Palindromic width of wreath products, metabelian groups, and max-n solvable groups
    with Andrew Sale, Groups – Complexity – Cryptology, pages 121–132, 6 (2), 2014. arXiv version

19. Cannon–Thurston maps, subgroup distortion, and hyperbolic hydra
    with Owen Baker, Groups Geom. Dyn. 14 (2020), no. 1, 255–282. arXiv version

20. Graham Higman's lectures on januarials
    with Martson Conder, The Quarterly Journal of Mathematics (Oxford), 65 (1), pages 113–131, 2014. arXiv version

21. Cannon–Thurston maps do not always exist
    with Owen Baker, Forum of Mathematics, Sigma, 1, e3 (11 pages), 2013. arXiv version

22. What is a Dehn function?
    Chapter for Office hours with a geometric group theorist,
    edited by Matt Clay and Dan Margalit, Princeton University Press, 2017. Preprint version

23. Hyperbolic hydra
    with Noel Brady and Will Dison, Groups, Geometry and Dynamics, pages 961–976, 7 (4), 2013. arXiv version

24. The Dehn function of Baumslag's metabelian group
    with Martin Kassabov, Geometriae Dedicata, pages 109–119, 158 (1), 2012. arXiv version

25. Hydra groups
    with Will Dison, Commentarii Mathematici Helvetici, 88(3), pages 507–540, 2013. arXiv version

26. The Dehn function of Stallings' group
    with Will Dison, Murray Elder and Robert Young, Geometric and Functional Analysis, 19(2), pages 406–422, 2009. arXiv version

27. Extrinsic versus intrinsic diameter for Riemannian filling-discs and van Kampen diagrams
    with Martin Bridson, Journal of Differential Geometry, 82(1), 115–154, 2009. arXiv version

28. The Dehn function of SLn(Z) (expository)
    L'Enseignement Mathématique, 40, "Guido's book of Conjectures", pages 156–158, 2008.  Preprint version  

29. Free and fragmenting filling length
    with Martin Bridson, Journal of Algebra, 307(1), pages 171–190, 2007. arXiv version

30. The absence of efficient dual pairs of spanning trees in planar graphs
    with Bill Thurston, Electronic J. Comb., 13, N13, 2006. arXiv version

31. Filling functions
    Part II of Geometry of the Word Problem for Finitely Generated Groups,
    Advanced Courses in Mathematics, CRM Barcelona, Birkhäuser-Verlag, 2007. Preprint version

32. The unbounded dead-end depth property is not a group invariant
    with Andrew Warshall, Int. J. Alg. Comp., 16(5), pages 969–984, 2006. arXiv version

33. Diameters of Cayley Graphs of Chevalley Groups
    with Martin Kassabov, Eur. J. Comb., 28(3), pages 791–800, 2007. Preprint version

34. Navigating in the Cayley Graphs of SL_N(Z) and SL_N(F_p)
    Geometriae Dedicata, 113(1), pages 215–229, 2005. arXiv version

35. A finitely presented group with unbounded dead-end depth
    with Sean Cleary, Proc. Amer. Math. Soc., 134(2), pages 343–349, 2006. arXiv version

36. Some duality conjectures for finite graphs and their group theoretic consequences
    with Steve Gersten, Proc. Edin. Math. Soc., 48(2), pages 389–421, 2005. Preprint version

37. The gallery length filling function and a geometric inequality for filling length
    with Steve Gersten, Proc. London Math. Soc., 92(3), pages 601–623, 2006. Preprint version

38. Isoperimetric inequalities for nilpotent groups
    with Steve Gersten and Derek Holt, Geometric And Functional Analysis , 13, pages 795–814, 2003. arXiv version

39. The geometry of groups satisfying weak almost-convexity or weak geodesic-combability conditions
    Journal of Group Theory, 5(4), pages 513–525, 2002. Preprint version

40. Higher connectedness of asymptotic cones
    Topology, 42, pages 1289–1352, 2003. Preprint version

41. Filling radii of finitely presented groups
    with Steve Gersten, Quarterly Journal of Mathematics (Oxford), 53(1), pages 31–45, 2002. Preprint version

42. Filling length in finitely presentable groups
    with Steve Gersten, Geometriae Dedicata, 92(1), pages 41–58, 2002. arXiv version

Doctoral Thesis. Asymptotic Invariants of Infinite Discrete Groups

Oxford University, 2002, supervised by Martin Bridson

Most of the content can be found in the 2003 Topology and 2002 Journal of Group Theory articles above.

Support from the U.S. National Science Foundation under Grants No. DMS0540830 (2004–2007), DMS1101651 (2011–2014), and GCR2428489 (2024–) is gratefully acknowledged. Any opinions, findings, and conclusions or recommendations expressed in these web pages are those of the author and do not necessarily reflect the views of the National Science Foundation.