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Fractional distortion in hyperbolic groups with Pallavi Dani Active learning taking root—a progress update with David Freund, Tara Holm, and Marie MacDonald, to appear in PRIMUS Exponentially distorted subgroups in wreath products Dehn functions of mapping tori of right-angled Artin groups with Kristen Pueschel, to appear in Glasgow J. Math The Generalized Dehn Property does not imply a linear isoperimetric inequality with Owen Baker, Ann. Math. Qué. 44 (2020), no. 1, 1–7 Soficity and variations on Higman's group with Martin Kassabov and Vivian Kuperberg, Journal of Combinatorial Algebra, 3(1), pages 41–70, 2019 Computing area in presentations of the trivial group Proc. Amer. Math. Soc. 145 (2017), 5059–5069 Ackermannian integer compression and the word problem for hydra groups with Will Dison and Eduard Einstein, Mathematical Foundations of Computer Science 2016 (Krakow) 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 Lamplighters, metabelian groups, and horocyclic products of trees with Margarita Amchislavska, L'Enseignement Mathématique, 61, pages 373–415, 2015 Palindromic width of wreath products, metabelian groups, and max-n solvable groups with Andrew Sale, Groups – Complexity – Cryptology, pages 121–132, 6 (2), 2014 Cannon–Thurston maps, subgroup distortion, and hyperbolic hydra with Owen Baker, Groups Geom. Dyn. 14 (2020), no. 1, 255–282 Graham Higman's lectures on januarials with Martson Conder, The Quarterly Journal of Mathematics (Oxford), 65 (1), pages 113–131, 2014 Cannon–Thurston maps do not always exist with Owen Baker, Forum of Mathematics, Sigma, 1, e3 (11 pages), 2013 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 Hyperbolic hydra with Noel Brady and Will Dison, Groups, Geometry and Dynamics, pages 961–976, 7 (4), 2013 The Dehn function of Baumslag's metabelian group with Martin Kassabov, Geometriae Dedicata, pages 109–119, 158 (1), 2012 Hydra groups with Will Dison, Commentarii Mathematici Helvetici, 88(3), pages 507–540, 2013 The Dehn function of Stallings' group with Will Dison, Murray Elder and Robert Young, Geometric and Functional Analysis, 19(2), pages 406–422, 2009 Extrinsic versus intrinsic diameter for Riemannian filling-discs and van Kampen diagrams with Martin Bridson, Journal of Differential Geometry, 82(1), 115–154, 2009 The Dehn function of SLn(Z) (expository) L'Enseignement Mathématique, 40, "Guido's book of Conjectures", pages 156–158, 2008 Free and fragmenting filling length with Martin Bridson, Journal of Algebra, 307(1), pages 171–190, 2007 The absence of efficient dual pairs of spanning trees in planar graphs with Bill Thurston, Electronic J. Comb., 13, N13, 2006 Filling functions Part II of Geometry of the Word Problem for Finitely Generated Groups, Advanced Courses in Mathematics, CRM Barcelona, Birkhäuser-Verlag, 2007 The unbounded dead-end depth property is not a group invariant with Andrew Warshall, Int. J. Alg. Comp., 16(5), pages 969–984, 2006. Diameters of Cayley Graphs of Chevalley Groups with Martin Kassabov, Eur. J. Comb., 28(3), pages 791–800, 2007 Navigating in the Cayley Graphs of SL_N(Z) and SL_N(F_p) Geometriae Dedicata, 113(1), pages 215–229, 2005 A finitely presented group with unbounded dead-end depth with Sean Cleary, Proc. Amer. Math. Soc., 134(2), pages 343–349, 2006 Some duality conjectures for finite graphs and their group theoretic consequences with Steve Gersten, Proc. Edin. Math. Soc., 48(2), pages 389–421, 2005 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 Isoperimetric inequalities for nilpotent groups with Steve Gersten and Derek Holt, Geometric And Functional Analysis , 13, pages 795–814, 2003 The geometry of groups satisfying weak almost-convexity or weak geodesic-combability conditions Journal of Group Theory, 5(4), pages 513–525, 2002 Higher connectedness of asymptotic cones Topology, 42, pages 1289–1352, 2003 Filling radii of finitely presented groups with Steve Gersten, Quarterly Journal of Mathematics (Oxford), 53(1), pages 31–45, 2002 Filling length in finitely presentable groups with Steve Gersten, Geometriae Dedicata, 92(1), pages 41–58, 2002	Articles on the ArXiv (incomplete) MathSciNet Reviews (subscription required) Graduate class blogs & notes Exploring the works of Gilbert Baumslag, 2015 The geometry of solvable groups, 2013 Here there be dragons: subgroups of non-positively curved groups, 2011

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 listed above.

Support from the U.S. National Science Foundation under Grants No. DMS0540830 (2004–2007) and DMS1101651 (2011–2014) 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.