(Mathematics) (Computer science) (Exposition and art) (Software) (Thesis)
If you have any trouble with the links below please inform me via email.

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Mathematics:

• Connecting essential triangulations II: via 2-3 moves only

  (arXiv) (Copyright) with Tejas Kalelkar and Henry Segerman.

  2024 preprint.

• Connecting essential triangulations I: via 2-3 and 0-2 moves

  (arXiv) (Copyright) with Tejas Kalelkar and Henry Segerman.

  2024 preprint.

• Excluding cosmetic surgeries on hyperbolic 3-manifolds

  (arXiv) (Copyright) with David Futer and Jessica Purcell.

  2024 preprint.

• From veering triangulations to dynamic pairs

  (arXiv) (Copyright) with Henry Segerman.

  2023 preprint.

• Large volume fibred knots of fixed genus

  (arXiv) (Copyright) with Kenneth L. Baker, David Futer, and Jessica Purcell.

  2022 preprint. To appear in Mathematical Research Letters.

• Recognising elliptic manifolds

  (arXiv) (Copyright) with Marc Lackenby.

  2022 preprint.

• Asymptotic dimensions of the arc graphs and disk graphs

  (arXiv) (Copyright) with Koji Fujiwara.

  Algebraic and Geometric Topology, 24 (2024), no. 5, 2655–2672.

• From loom spaces to veering triangulations

  (arXiv) (Copyright) with Henry Segerman.

  Groups, Geometry, and Dynamics, 18 (2024), no. 2, 419–462.

• Hard diagrams of the unknot

  (arXiv) (Copyright) with Benjamin A. Burton, Hsien-Chih Chang, Maarten Löffler, Arnaud de Mesmay, Clément Maria, Eric Sedgwick, and Jonathan Spreer.

  Experimental Mathematics, 33 (2024), no. 3, 482–500.

• Effective drilling and filling of tame hyperbolic three-manifolds

  (PDF) (arXiv) (Copyright) with David Futer and Jessica Purcell.

  Commentarii Mathematici Helvetici, 97 (2022), no. 3, 457–512.

• Diagonal flow detects topology of strata

  (arXiv) (Copyright) with Mark Bell. Vincent Delecroix, Vaibhav Gadre, and Rodolfo Gutiérrez-Romo.

  2024 preprint.

• Quotients of the curve complex

  (arXiv) (Copyright) with Joseph Maher and with Hidetoshi Masai.

  Groups, Geometry, and Dynamics, 18 (2024), no. 2, 379–405.

• Cohomology fractals, Cannon-Thurston maps, and the geodesic flow

  (PDF) (arXiv) (Copyright) with David Bachman, Matthias Goerner, and Henry Segerman

  Experimental Mathematics, 31 (2022), no. 4, 1047–1085.

• From veering triangulations to link spaces and back again

  (arXiv) (Copyright) with Steven Frankel and Henry Segerman.

  2019 preprint.

• Coding Teichmüller flow using veering triangulations

  (arXiv) (Copyright) with Mark Bell. Vincent Delecroix, Vaibhav Gadre, and Rodolfo Gutiérrez-Romo.

  2019 preprint.

• Effective bilipschitz bounds on drilling and filling

  (PDF for screen) (PDF for printing) (arXiv) (Copyright) with David Futer and Jessica Purcell.

  Geometry and Topology, 26 (2022), no. 3, 1077–1188.

• Essential loops in taut ideal triangulations

  (PDF for screen) (PDF for printing) (arXiv) (Copyright) with Henry Segerman.

  Algebraic and Geometric Topology, 20 (2020), no. 1, 487–501.

• On the tree-width of knot diagrams

  (PDF) (arXiv) (Copyright) with Arnaud de Mesmay, Jessica Purcell, and Eric Sedgwick.

  Journal of Computational Geometry, 10 (2019), no. 1, 164–180.

• Compressed decision problems in hyperbolic groups

  (arXiv) (Copyright) with Derek Holt and Markus Lohrey.

  2018 preprint.
  Journal version: To appear in Groups, Geometry, and Dynamics.
  Conference version: 36th International Symposium on Theoretical Aspects of Computer Science, 126 (2019), 37:1–37:16.

• Garside theory and subsurfaces: some examples in braid groups

  (arXiv) (Copyright) with Bert Wiest.

  Groups Complexity Cryptology, 11 (2019), no. 2, 61–75.

• Groups whose word problems are not semilinear

  (arXiv) (Copyright) with Robert Gilman and Robert Kropholler.

  Groups Complexity Cryptology, 10 (2018), no. 2, 53–62.

• The compression body graph has infinite diameter

  (arXiv) (Copyright) with Joseph Maher.

  Algebraic and Geometric Topology, 21 (2021), no. 4, 1817–1856.

• Effective distance between nested Margulis tubes

  (arXiv) (Copyright) with David Futer and Jessica Purcell.

  Transactions of the American Mathematical Society, 372 (2019), no. 6, 4211–4237.

• Tightening curves on surfaces via local moves

  (Copyright) with Hsien-Chih Chang, Jeff Erickson, David Letscher, Arnaud de Mesmay, Eric Sedgwick, Dylan Thurston, and Stephan Tillmann.

  Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms, 121–135, SIAM, Philadelphia, PA, 2018.

• Slow north-south dynamics on PML

  (arXiv) (Copyright) with Mark Bell.

  Groups, Geometry, and Dynamics, 11 (2017), no. 3, 1103–1112.

• The curves not carried

  (arXiv) (Copyright) with Vaibhav Gadre.

  Groups, Geometry, and Dynamics, 10 (2016), no. 4, 1249–1264.

• Uniform hyperbolicity of the curve graph via surgery sequences

  (PDF) (arXiv) (Copyright) with Matt Clay and Kasra Rafi.

  Algebraic and Geometric Topology, 14 (2014), no. 6, 3325–3344.

• Hyperbolic spaces in Teichmüller spaces

  (PDF) (arXiv) (Copyright) with Christopher Leininger.

  Journal of the European Mathematical Society, 16 (2014), no. 12, 2669–2692.

• Cusp geometry of fibered three-manifolds

  (PDF) (arXiv) (Copyright) with David Futer.

  American Journal of Mathematics, 136 (2014), no. 2, 309–356.

• The geometry of the disk complex

  (PDF) (Out-of-date version at the arXiv) (Copyright) with Howard Masur.

  Journal of the American Mathematical Society, 26 (2013), no. 1, 1–62.

• On train-track splitting sequences

  (PDF) (arXiv) (Copyright) with Howard Masur and Lee Mosher.

  Duke Mathematical Journal, 161 (2012), no. 9, 1613–1656.

• Automorphisms of the disk complex

  (PDF) (Out-of-date version at the arXiv) (Copyright) with Mustafa Korkmaz.

  2009 preprint.

• Dehn twists have roots

  (PDF) (arXiv) (Copyright) with Dan Margalit.

  Geometry and Topology, 13 (2009), no. 3, 1495–1497.

• The universal Cannon-Thurston map and the boundary of the curve complex

  (PDF) (arXiv) with Christopher Leininger and Mahan Mj.

  Commentarii Mathematici Helvetici, 86 (2011), no. 4, 769–816.

• Canonical triangulations of Dehn fillings

  (PDF) (arXiv) (Copyright) with Francois Gueritaud.

  Geometry and Topology, 14 (2010), no. 1, 193–242.

• Connectivity of the space of ending laminations

  (PDF) (arXiv) with Christopher Leininger.

  Duke Mathematical Journal, 150 (2009), no. 3, 533–575.

• Curve complexes are rigid

  (PDF) (Out-of-date version at the arXiv) (Copyright) with Kasra Rafi.

  Duke Mathematical Journal, 158 (2011), no. 2, 225–246.

• Geodesic ideal triangulations exist virtually

  (PDF) (arXiv) (Copyright) with Feng Luo and Stephan Tillmann.

  Proceedings of the American Mathematical Society, 136 (2008), no. 7, 2625–2630.

• Covers and the curve complex

  (PDF) (Out-of-date version at the arXiv) (Copyright) with Kasra Rafi.

  Geometry and Topology, 13 (2009), no. 4, 2141–2162.

• Trees and mapping class groups

  (PDF) (arXiv) (Copyright) with Richard Kent IV and Christopher Leininger.

  Journal fur die reine und angewandte Mathematik, 637 (2009), 1–21.

• The end of the curve complex

  (PDF) (Out-of-date version at the arXiv) (Copyright).

  Groups, Geometry, and Dynamics, 5 (2011), no. 1, 169–176.

• High distance knots

  (PDF) (arXiv) (Copyright) with Yair Minsky and Yoav Moriah.

  Algebraic and Geometric Topology, 7 (2007), no. 3, 1471–1483.

• Polynomial-time word problems

  (PDF) (Out-of-date version at the arXiv) (Copyright).

  Commentarii Mathematici Helvetici, 83 (2008), no. 4, 741–765.

• Sweepouts of amalgamated three-manifolds

  (arXiv) (Copyright) with David Bachman and Eric Sedgwick.

  Algebraic and Geometric Topology, 6 (2006), no. 1, 171–194.

• Heegaard splittings of the form H + nK

  (PDF) (Out-of-date version at the arXiv) (Copyright) with Yoav Moriah and and Eric Sedgwick.

  Communications in Analysis and Geometry, 14 (2006), no. 2, 215–247.

• Sphere recognition lies in NP

  (PDF) (Out-of-date version at the arXiv) (Abstract) (Comments) (Copyright).

  Low-Dimensional and Symplectic Topology, Proceedings of Symposia in Pure Mathematics, 82 (2011), 183–213.

• The pants complex has only one end

  (PDF) (Out-of-date version at the arXiv) (Copyright) with Howard Masur.

  Spaces of Kleinian groups, London Mathematical Society Lecture Note Series, 329 (2006), 209–218.

• Distance and bridge position

  (PDF) (arXiv) (Copyright) with David Bachman.

  Pacific Journal of Mathematics, 219 (2005), no. 2, 221–235.

• Distances of Heegaard splittings

  (arXiv) (Copyright) with Aaron Abrams.

  Geometry and Topology, 9 (2005), 95–119.

• Surface bundles versus Heegaard splittings

  (PDF) (Out-of-date version at the arXiv) (Copyright) with David Bachman.

  Communications in Analysis and Geometry, 13 (2005), no. 5, 903–928.

• The disjoint curve property

  (arXiv) (Abstract) (Comments) (Copyright).

  Geometry and Topology, 8 (2004), 77–113.

• Thin position for tangles

  (arXiv) (Abstract) (Copyright) with David Bachman.

  Journal of Knot Theory and its Ramifications, 12 (2003), no. 1, 117–122.

• Strongly irreducible surface automorphisms

  (arXiv) (Copyright) .

  Topology and geometry of manifolds, Proceedings of Symposia in Pure Mathematics, 71 (2003), 287–296.

• On the girth of groups

  (PDF) (Copyright)

  2000 preprint.

• Computing triangulations of mapping tori of surface homeomorphisms

  (PDF) (arXiv) (Abstract) (Errata) (Copyright) with Peter Brinkmann.

  Experimental Mathematics, 10 (2001), no. 4, 571–581.

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Computer science:

• Winnowing: Local algorithms for document fingerprinting

  (PDF) (Abstract) (Patent) (Errata) (Copyright) with Alex Aiken and Daniel Wilkerson.

  ACM Special Interest Group on Management of Data, 2003.

• System area network mapping

  (PDF) (Copyright) with Brent Chun, Alan Mainwaring, and Daniel Wilkerson.

  ACM Symposium on Parallel Algorithms and Architectures, 1997.

• Nearly tight bounds for wormhole routing

  (PDF) (Copyright) with Abhiram Ranade and Daniel Wilkerson.

  IEEE Symposium on Foundations of Computer Science, 1994.

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Exposition and art:

• Cohomology fractals

  (Bridges archive) (arXiv) (Copyright) with David Bachman and Henry Segerman.

  Proceedings of Bridges 2020: Mathematics, Music, Art, Architecture, Culture, (2020) 175–182.

• Conformally correct tilings

  (Book) (arxiv) (Copyright) with Henry Segerman.

  Book chapter, Objets mathématiques, (2017), Paris: CNRS Editions.

• Squares that look round: transforming spherical images

  (Bridges archive) (arxiv) (Copyright) with Henry Segerman.

  Proceedings of Bridges 2016: Mathematics, Music, Art, Architecture, Culture, (2016) 15–24.

• Puzzling the 120–cell

  (PDF) (Long version at the arXiv) (Abstract) (Links) (Copyright) with Henry Segerman.

  Notices of the American Mathematical Society, (2015) 1309–1316.

• Triple gear

  (Bridges archive) (arXiv) (Abstract) (Links) (Copyright) with Henry Segerman.

  Proceedings of Bridges 2013: Mathematics, Music, Art, Architecture, Culture, (2013) 353–360.

• Sculptures in $S^3$

  (Bridges archive) (PDF) (arXiv) (Copyright) with Henry Segerman.

  Proceedings of Bridges 2012: Mathematics, Music, Art, Architecture, Culture, (2012) 103–110.

• Waldhausen's theorem

  (PDF) (arXiv) (Copyright).

  Geometry & Topology Monographs, 12 (2007) 299–317.

• Notes on the complex of curves

  (PDF) (Web site) (Copyright)

  Caltech, minicourse Jan. 2005 (revised 2020-04-23).

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Software:

• Veering

  (Github) with Anna Parlak and Henry Segerman

  Regina-python and sage code for working with transverse taut and veering ideal triangulations.

• Cohomology fractals

  (Web app) (Youtube explainer) (Youtube zooms) (Github) with Henry Segerman and David Bachman.

  Web app for exploring cohomology fractals. All hyperbolic manifolds from the orientable cusped census (with at most seven tetrahedra) are available.

• Twister

  (Abstract) with Mark Bell and Tracy Hall.

  Builds triangulated three-manifolds based on Dehn twist or Heegaard data.

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Thesis:

• Almost normal Heegaard splittings

  (PDF) (Abstract) (Errata) (Copyright).

  2001 Ph.D. thesis.

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Last time this line was updated: Thu 24 Jun 2021 11:00:50 BST

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Homepage: To maintainer's homepage.

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Warwick: Up to the math department webpage.