Research Articles
My research articles are listed below, roughly by topic. Click on a title to download. You can also find my papers on the arXiv.
Click here for a list of papers in (reverse) chronological order.
Complex dynamics
Recognizing topological polynomials by lifting trees
-----w/ Jim Belk, Justin Lanier, and Becca Winarski
-----Duke Mathematical Journal, 171 (2022) no.17, p. 3401-3480.
Thurston’s theorem and the Nielsen–Thurston classification via Teichmüller’s theorems
-----w/ Jim Belk and Becca Winarski
-----submitted
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Torelli groups
The dimension of the Torelli group
-----w/ Mladen Bestvina and Kai-Uwe Bux
-----Journal of the AMS 23 (2010), no. 1, 61-105.
Generating the Torelli group
-----w/ Allen Hatcher
-----L'Enseignement Mathématique 58 (2012), 165-188.
Dimension of the Torelli group for Out(Fn)
-----w/ Mladen Bestvina and Kai-Uwe Bux
-----Inventiones Mathematicae 170 (2007), no. 1, 1-32.
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Hyperelliptic Torelli groups
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.
Representation stability in the level four braid group
-----w/ Kevin Kordek
-----Mathematische Zeitschrift 302, p. 433-482, 2022.
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
Factoring in the hyperelliptic Torelli group
-----w/ Tara Brendle
-----Mathematical Proceedings of the Cambridge Philosophical Society, 159 (02), 207-217, 2015.
Point pushing, homology, and the hyperelliptic involution
-----w/ Tara Brendle
-----Michigan Mathematical Journal 62(3), 451-473, 2013.
Cohomology of the hyperelliptic Torelli group
-----w/ Tara Brendle and Leah Childers
-----Israel Journal of Mathematics, 195, 613-630, 2013.
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Automorphisms of Mapping Class Groups and Curve Complexes
Automorphisms of the fine curve graph
-----w/ Adele Long, Anna Pham, Yvon Verberne, and Claudia Yao
-----Transactions of the American Mathematical Society, to appear
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.
Normal subgroups of mapping class groups and the metaconjecture of Ivanov
-----w/ Tara Brendle
-----Journal of the AMS, 32 (4) 1009-1070, 2019.
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.
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.
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.
Addendum to: Commensurations of the Johnson kernel
-----w/ Tara Brendle
-----Geometry and Topology 12 (2008), 97-101.
Erratum to: Commensurations of the Johnson kernel
-----w/ Tara Brendle
-----Submitted
Automorphisms of the pants complex
-----Duke Mathematical Journal 121(3):
457-479, 2004.
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Pseudo-Anosov Stretch Factors
Normal generators for mapping class groups are abundant
-----w/ Justin Lanier
-----Commentarii Mathematici Helvetici 97, 1-59, 2022.
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.
On the number and location of short geodesics in moduli space
-----w/ Chris Leininger
-----Journal of Topology, 6(1), 30-48, 2013.
Small dilatation pseudo-Anosov homeomorphisms and 3-manifolds
-----w/ Benson Farb and Chris Leininger
-----Advances in Mathematics, 228(3): 1466-1502, 2011.
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.
A homological recipe for pseudo-Anosovs
-----w/ Steven Spallone
-----Mathematical Research Letters 14 (2007), no.5, 853-863.
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Geometry of the Complex of Curves
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.
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Stable commutator length
Surface groups, infinite generating sets, and stable commutator length
-----w/ Andy Putman
-----Proceedings A of the Royal Society of Edinburgh, to appear
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Relations in Mapping Class Groups
Right-angled Artin groups as normal subgroups of mapping class groups
-----w/ Matt Clay and Johanna Mangahas
-----Compositio Mathematica, 157, no. 8, 1807-1852, 2021.
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.
A lantern lemma
-----Alg. and Geom. Topology 2: 1179-1195 2002.
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Lefschetz Fibrations
Lefschetz fibrations and Torelli groups
-----w/ Inanc Baykur
-----Geometriae Dedicata 177 (1), 275-291, 2015.
Indecomposable surface bundles over surfaces
-----w/ Inanc Baykur
-----Journal of Topology and Analysis 5(2), 161-181, 2013.
Expository Articles
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
Mixing Surfaces, Algebra, and Geometry
-----Notices of the American Mathematical Society, May 2023.
-----Click here for the accompanying animations
The Mathematics of Joan Birman
-----Notices of the American Mathematical Society, March 2019.
-----Winner of the 2021 Levi L. Conant Prize.
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.
The Birman-Hilden theory
-----w/ Rebecca Winarski
-----Celebratio Mathematica and
-----Bulletin of the London Mathematical Society 53 (3), 643-659, 2021.
Thurston’s Work on Surfaces (book review)
-----Bulletin of the AMS 51 (1), 151-161, 2014.
A Carnival of Calculus
---MAA Focus, May 2008