Publications and Preprints
All of my papers and preprints are stored on arXiv.org, and the papers there are
the definitive versions. They are identical in content to the
published versions except where the journal introduced errors
(e.g. the hilarious references to "Inventory Mathematics" in the
published version of paper 2).
Publications and preprints
 With N. Brown and G. Perry. Colorings of the plane. Parts I,
II, and III. Geombinatorics 3 (1993), no. 2,
2431; 3 (1994), no. 3, 6474; 3 (1994), no. 4,
110114.
 Examples of nontrivial roots of unity at ideal
points of hyperbolic 3manifolds. Topology
38 (1999), 457  465.
math.GT/9801064.
 Cyclic surgery, degrees of maps of character curves,
and volume rigidity for hyperbolic manifolds.
Invent. Math. 136 (1999) 3, 623657.
math.GT/9802022.
 A table of boundary slopes of Montesinos knots.
Topology, 40 (2001) 2, 309315.
math.GT/9901120. Associated software.
 Alexander and Thurston norms of fibered
3manifolds. Pacific
J. Math. 200 (2001), 4358.
math.GT/9908050.
 With Danny Calegari. Commensurability of 1cusped hyperbolic
3manifolds. Trans. Amer. Math. Soc. 354 (2002), 29212932.
math.GT/0102024.
 With Danny Calegari. Laminations and groups of
homeomorphisms of the circle. Invent. Math. 152 (2003) 149207.
math.GT/0203192.
 With Bill Thurston. The Virtual Haken Conjecture:
Experiments and Examples. Geom. Topol. 7
(2003) 399441.
math.GT/0209214.
Associated software and data.
 With Stavros Garoufalidis. Nontriviality of the
Apolynomial for knots in the 3sphere.
Algebr. Geom. Topology 4 (2004), 11451153.
math.GT/0405353.
 The Mahler measure of the Apolynomial of m129(0,3).
Appendix to D. Boyd and F. Rodriguez Villegas, Mahler's measure and
the dilogarithm (II).
math.NT/0308041.
 With Danny Calegari. An ascending HNN extension of a free group
inside SL(2,C). Proc. Amer. Math. Soc. 134 (2006)
31313136. math.GR/0412136.
 With Bill Thurston. Finite covers of random
3manifolds. Invent. Math. 166 (2006) 457521.
math.GT/0502567.
 With Sergei Gukov and Jake Rasmussen. The superpolynomial
for knot homologies. Experimental Math.
15 (2006), 129159.
math.GT/0505662.
 Volume change under drilling: theory vs. experiment.
Appendix to Agol, Storm, and W. Thurston, Lower bounds on
volumes of hyperbolic Haken 3manifolds,
J. Amer. Math. Soc. 20 (2007), 10531077.
math.DG/0506338.
 With Frank Calegari. Automorphic forms and rational
homology 3spheres, Geom. Topol. 10 (2006) 295329.
math.GT/0508271.
Associated data.
 With Dylan Thurston. A random tunnel number one 3manifold
does not fiber over the circle. Geom. Topol.
10 (2006) 24312499.
math.GT/051029.
 With S. Garoufalidis, A. Shumakovitch, and M. Thistlethwaite.
Behavior of knot invariants under genus 2 mutation.
New York J. Math., 16 (2010) 99123.
math.GT/0607258.
 With Dinakar Ramakrishnan. Increasing the number of
fibered faces of arithmetic hyperbolic 3manifolds.
Amer. J. Math 132 (2010), 5397.
arXiv:0712.3243.
Associated software and data.
 With John W. Aaber. Closed surface bundles of least
volume, Algebr. Geom. Topology 10 (2010), 23152342.
arXiv:1002.3423.
 With Helen Wong. Quantum invariants of random
3manifolds, Algebr. Geom. Topology 11
(2011) 21912205. arXiv:1009.1653.
 With Anil Hirani. The Least Spanning Area of a Knot and
the Optimal Bounding Chain Problem, SoCG 2011: Proceedings of the
27th annual ACM symposium on Computational Geometry, pages 135144.
arXiv:1012.303.
 With Stavros Garoufalidis. Incompressibility criteria for
spunnormal surfaces, Trans. Amer. Math. Soc.
64 (2012) 61096137.
arXiv:1102.4588.
 With Stefan Friedl and Nicholas Jackson. Twisted Alexander
polynomials of hyperbolic knots, Experimental
Math. 21 (2012) 329352.
arXiv:1108.3045.
Associated software and data.
 With Jeff Brock. Injectivity radii of hyperbolic integer
homology 3spheres, Geom. Topol. 19 (2015), 497523.
arXiv:1304.0391.
 With Neil Hoffman and Joan Licata. Asymmetric hyperbolic
Lspaces, Heegaard genus, and Dehn filling,
Math. Res. Letters, 22 (2015) 16791698.
arXiv:1407.7827.
 A diffuse group which is not leftorderable. Appendix to Kionke and
Raimbault, On geometric aspects of diffuse groups,
Documenta Math. 21 (2016) 873915.
arXiv:1411.6449.
 With Ian Agol. Certifying the Thurston norm via SL(2,
C)twisted homology, What's next? The Mathematical Legacy of William
P. Thurston, Ann. of Math. Studies 205 (2020), 120,
Princeton Univ. Press.
arXiv:1501.02136.
 A knot without a nonorientable essential spanning
surface, Illinois J. Math. 60 (2016) 179184.
arXiv:1509.06653.
 With Jeff Brock. Norms on the cohomology of hyperbolic 3manifolds,
Invent. Math. 210 (2017) 531558.
arXiv:1510.06292.
 With Marc Culler. Orderability and Dehn filling,
Geom. Topol. 22 (2018) 14051457.
arXiv:1602.03793.
 A census of exceptional Dehn fillings,
Characters in lowdimensional topology,
Contemp. Math. 760 (2020) 143155.
arXiv:1812.11940.
 Floer homology, group orderability, and taut foliations
of hyperbolic 3manifolds,
Geom. Topol. 24 (2020), 20752125.
arXiv:1904.04628.
 With Stavros Garoufalidis and J. Hyam Rubinstein.
Counting essential surfaces in 3manifolds,
Invent. Math. 228 (2022), 717775.
arXiv:2007.10053.
 S. Peddada, N. Dunfield, L. Zeidner, K. James, and J. Allison,
Systematic Enumeration and Identification of Unique Spatial
Topologies of 3D Systems Using Spatial Graph Representations,
Proceedings of the ASME 2021 International Design Engineering
Technical Conferences & Computers and Information in Engineering
Conference, Volume 3A: 47th Design Automation Conference (DAC), 13 pages.
arXiv:2107.13724.

With Cameron Rudd and Malik Obeidin.
Computing a Link Diagram from its Exterior,
Proceedings of the 38th International Symposium on Computational
Geometry (SoCG 2022), pages 37:137:24.
arXiv:2112.03251.
 With Jacob Rasmussen. A unified CassonLin invariant for
the real forms of SL(2). Preprint, 147 pages.
arXiv:2209.03382.
 Which small volume hyperbolic 3manifolds are Haken?
PDF or PostScript (Warwick, 1999).
 Does a random tunnelnumber one 3manifold fiber over the circle?
PDF or PostScript (Treiste 2005).
 Mathematical Truths: Experiment, Proof, and Understanding.
PDF (From a public lecture at Bowdoin Collge in 2007).
 Surfaces in finite covers of 3manifolds: the Virtual Haken
Conjecture: PDF (Single), PDF (Double). (Invited address at the AMS meeting in Raleigh, April 2009.)
 Practical solutions to hard problems in 3dimensional topology: PDF (Single), PDF (Double) (Hamilton Geometry and Topology Workshop, September 2009.)
 Hyperbolically twisted Alexander polynomials of knots: PDF (Single), PDF (Double) (Jacofest, June 2010)
 The Least Spanning Area of a Knot and the Optimal Homologous
Chain Problem: PDF (Single), PDF (Double) (SoCG, Paris, June 2011)
 The Least Spanning Area of a Knot and the Optimal Homologous
Chain Problem: PDF (Single), PDF (Double) (Hyamfest, July 2011)
 Hyperbolically twisted Alexander polynomials of knots
: PDF (Single), PDF (Double). Complete
video. (CBMSNSF Conference, NYC, August 2011)
 Hyperbolically twisted Alexander polynomials of knots
: PDF (Single), PDF (Double). (Gauge Theory Seminar,
Harvard, April 2012)
 Hyperbolic geometry of integer homology 3spheres.
Complete
video. (Banff, July 2012)
 Surfaces in finite covers of 3manifolds: the Virtual Haken
Conjecture Complete
video. (GEAR retreat, Urbana, August 2012)
 Lspaces and leftorderability: an experimental survey.
Complete
video. (Banff, April 2013)
 Integer homology 3spheres with large injectivity radius.
Complete
video. (GTiNY2013, Columbia University, July 2013)
 Practical computation with hyperbolic 3manifolds. Complete
video. (Thurston Memorial Conference, Cornell, June 2014)
 Computational complexity of problems in 3dimensional
topology. PDF slides. Complete
video.
(Combinatorial Link Homology Theories, Braids, and Contact Geometry,
ICERM, August 2014)
 What does a random 3manifold look like? PDF slides.
(Combinatorial Link Homology Theories, Braids, and Contact Geometry, ICERM, August 2014)
 Random knots: a preliminary report. PDF slides. (Various conferences, Fall
2014)
 Certifying the Thurston norm via twisted homology. Complete video.
(GGD/GEAR Seminar, January 2015)
 A tale of two norms. Complete video.
(New Developments in TQFT, CQM, Aarhus, July 2015)
 A tale of two norms. Complete video.
(GGD/GEAR Seminar, August 2015)
 Fun with finite covers of 3manifolds: topology, geometry and arithmetic. Complete video.
(IAS members' seminar, Nov 2015)
 Floer homology, group orders, and taut foliations of hyperbolic
3manifolds: an experimental survey. Slides. Complete video
(Flows, Foliations and Contact Structures, IAS, Dec 2015)
 Floer homology, group orders, and taut foliations of hyperbolic
3manifolds: an experimental survey. Slides. Complete video
(Interactions of Gauge Theory with Contact and Symplectic Topology in Dimensions 3 and 4, Banff, March 2016)
 Orderability and Dehn filling. Complete
video. (Geometric Group Theory and LowDimensional Topology, ICTP,
Trieste, June 2016)
 Three lecture series at the 33rd Annual Workshop in Geometric
Topology, held at Colorado College in June 2016. Same topics as talks
2024. Complete video.
 Floer homology, group orders, and taut foliations of hyperbolic
3manifolds: an experimental survey. Slides. Complete video
(3manifold workshops, Newton Institute, Jan 2017)
 Computation of geometric structures, part of a LMSCMI Research
School at Warwick, September 2017. Course webpage.
 Practical computations with hyperbolic 3manifolds,
Modularity and 3manifolds,
ICERM, March 2019: resources and
complete video.
 Computation Demonstration #2,
Perspectives on Dehn Surgery,
ICERM, July 2019: resources and
complete video.
 Illustrating 3dimensional topology and geometry,
Illustrating Geometry and Topology,
ICERM, September 2019: slides and
complete video.
 Counting incompressible surfaces in threemanifolds, Geometry and Topology Online (GaTO), May 2020.
slides
and complete video.
 Counting incompressible surfaces in threemanifolds, Virtual Seminar on
Geometry and Topology (VISGAT), June 2020.
slides.
 Harmonic 1forms on hyperbolic 3manifolds: connections and computations, MSRI, Nov 2020.
slides
and complete video.
 Counting incompressible surfaces in
threemanifolds, CMO, June 2021.
slides and
and
complete video.
Miscellaneous unpublished work
 An interesting relationship between the Jones polynomial and hyperbolic
volume. Web (2000).