My research articles are listed below, roughly by reverse chronological order. Click on a title to download. You can also find my papers on the arXiv.

Click here for a list of papers by area.

Quadratic-time computations for pseudo-Anosov mapping classes
-----w/ Balázs Strenner, Sam Taylor, and Öykü Yurttaş
-----preprint

Totally symmetric sets
-----w/ Noah Caplinger
-----to appear in Topology at infinity of discrete groups (Volume in honor of Mike Mihalik's 70th birthday), AMS series Contemporary Mathematics

Thurston’s theorem and the Nielsen–Thurston classification via Teichmüller’s theorems
-----w/ Jim Belk and Becca Winarski
-----submitted

Mixing Surfaces, Algebra, and Geometry
-----Click here for the accompanying animations
-----Notices of the American Mathematical Society, May 2023.

Automorphisms of the fine curve graph
-----w/ Adele Long, Anna Pham, Yvon Verberne, and Claudia Yao
-----Transactions of the American Mathematical Society, to appear

Recognizing topological polynomials by lifting trees
-----w/ Jim Belk, Justin Lanier, and Becca Winarski
-----Duke Mathematical Journal, 171 (2022) no.17, p. 3401-3480.

Homomorphisms between braid groups
-----w/ Lei Chen and Kevin Kordek
-----preprint.

Homomorphisms of commutator subgroups of braid groups
-----w/ Kevin Kordek
-----Bulletin of the London Mathematical Society, 54 (1) 95-111, 2022.

Representation stability in the level four braid group
-----w/ Kevin Kordek
-----Mathematische Zeitschrift, 302, p. 433-482, 2022.

Normal generators for mapping class groups are abundant
-----w/ Justin Lanier
-----Commentarii Mathematici Helvetici 97, 1-59, 2022.

Right-angled Artin groups as normal subgroups of mapping class groups
-----w/ Matt Clay and Johanna Mangahas
-----To appear in Compositio Mathematica, 157, no. 8, 1807-1852, 2021

The Mathematics of Joan Birman
-----Notices of the American Mathematical Society, March 2019.
-----Winner of the 2021 Levi L. Conant Prize.

Surface groups, infinite generating sets, and stable commutator length
-----w/ Andy Putman
-----Proceedings A of the Royal Society of Edinburgh, to appear

Problems, questions, and conjectures about mapping class groups
-----Breadth in contemporary topology: 2017 Georgia International Topology Conference, Proc. Sympos. Pure Math. 102, 157-186, 2019.

Normal subgroups of mapping class groups and the metaconjecture of Ivanov
-----w/ Tara Brendle
-----Journal of the AMS 32 (4), 1009-1070, 2019.

Erratum to: Commensurations of the Johnson kernel
-----w/ Tara Brendle
-----Geometry & Topology, to appear

The level four braid group
-----w/ Tara Brendle
-----Journal für die reine und angewandte Mathematik, 735, 249-264, 2018.

Corrigendum to: The level four braid group
-----w/ Tara Brendle
-----submitted

The Birman-Hilden theory
-----w/ Rebecca Winarski
-----Celebratio Mathematica and
-----Bulletin of the London Mathematical Society 53 (3), 643-659, 2021

Pseudo-Anosov stretch factors and homology of mapping tori
-----w/ Ian Agol and Chris Leininger
-----Journal of the London Mathematical Society 93 (3), 664-682, 2016.

Efficient geodesics and an effective algorithm for distance in the complex of curves
-----w/ Joan Birman and Bill Menasco
-----Mathematische Annalen 366(3), 1253-1279, 2016.

Generators for the hyperelliptic Torelli group and the kernel of the Burau representation at t = −1
-----w/ Tara Brendle and Andy Putman
-----Inventiones Mathematicae 200 (1) p. 263-310, 2015.

Factoring in the hyperelliptic Torelli group
-----w/ Tara Brendle
-----Mathematical Proceedings of the Cambridge Philosophical Society, 159 (02), 207-217, 2015.

Lefschetz fibrations and Torelli groups
-----w/ Inanc Baykur
-----Geometriae Dedicata 177 (1), 275-291, 2015.

Thurston’s Work on Surfaces (book review)
-----Bulletin of the AMS 51 (1), 151-161, 2014.

Abstract commensurators of right-angled Artin groups and mapping class groups
-----w/ Matt Clay and Chris Leininger
-----Mathematical Research Letters 21 (3) 461-467, 2014.

Point pushing, homology, and the hyperelliptic involution
-----w/ Tara Brendle
-----Michigan Mathematical Journal 62(3), 451-473, 2013.

On the number and location of short geodesics in moduli space
-----w/ Chris Leininger
-----Journal of Topology, 6(1), 30-48, 2013.

Cohomology of the hyperelliptic Torelli group
-----w/ Tara Brendle and Leah Childers
-----Israel Journal of Mathematics, 195, 613-630, 2013.

Indecomposable surface bundles over surfaces
-----w/ Inanc Baykur
-----Journal of Topology and Analysis 5(2), 161-181, 2013.

Generating the Torelli group
-----w/ Allen Hatcher
-----L'Enseignement Mathématique 58 (2012), 165-188.

Small dilatation pseudo-Anosov homeomorphisms and 3-manifolds
-----w/ Benson Farb and Chris Leininger
-----Advances in Mathematics, 228(3): 1466-1502, 2011.

The dimension of the Torelli group
-----w/ Mladen Bestvina and Kai-Uwe Bux
-----Journal of the AMS 23 (2010), no. 1, 61-105.

Two-generator subgroups of the pure braid group
-----w/ Chris Leininger
-----Geometriae Dedicata 147(1): 107-113, 2010.

Dehn twists have roots
-----w/ Saul Schleimer
-----Geometry and Topology 13 (2009), 1495-1497.

Geometric presentations for the pure braid group
-----w/ Jon McCammond
-----Journal of Knot Theory and Its Ramifications 18 (2009), no. 1, 1-20.

Addendum to: Commensurations of the Johnson kernel
-----w/ Tara Brendle
-----Geometry and Topology 12 (2008), 97-101.

The lower central series and pseudo-Anosov dilatations
-----w/ Benson Farb and Chris Leininger
-----The American Journal of Mathematics 130 (2008), no. 3, 799-827.

Dimension of the Torelli group for Out(F_n)
-----w/ Mladen Bestvina and Kai-Uwe Bux
-----Inventiones Mathematicae 170 (2007), no. 1, 1-32.

Injections of Artin groups
-----w/ Robert Bell
-----Commentarii Mathematici Helvetici, 82 (2007) 725-751.

Weil-Petersson isometries via the pants complex
-----w/ Jeff Brock
----- Proceedings of the AMS 135 (2007), 795-803.

A homological recipe for pseudo-Anosovs
-----w/ Steven Spallone
-----Mathematical Research Letters 14 (2007), no.5, 853-863.

Braid groups and the co-Hopfian property
-----w/ Robert Bell
-----Journal of Algebra 303: 275-294, 2006.

Abstract commensurators of braid groups
-----w/ Chris Leininger
-----Journal of Algebra 299 (2): 447-455, 2006.

Curve complexes and finite index subgroups of mapping class groups
-----w/ Jason Behrstock
-----Geometriae Dedicata 118(1): 71-85, 2006.

Commensurations of the Johnson kernel
-----w/ Tara Brendle
-----Geometry and Topology 4:1361-1384, 2004.

Automorphisms of the pants complex
-----Duke Mathematical Journal 121(3): 457-479, 2004.

A lantern lemma
-----Alg. and Geom. Topology 2: 1179-1195 2002.