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,
24-31; 3(1994), no. 3, 64-74; 3 (1994), no. 4,
110-114.
- Examples of non-trivial roots of unity at ideal
points of hyperbolic 3-manifolds. 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, 623-657.
math.GT/9802022.
- A table of boundary slopes of Montesinos knots.
Topology, 40 (2001) 2, 309-315.
math.GT/9901120. Associated software.
- Alexander and Thurston norms of fibered
3-manifolds. Pacific
J. Math. 200 (2001), 43-58.
math.GT/9908050.
- With Danny Calegari. Commensurability of 1-cusped hyperbolic
3-manifolds. Trans. Amer. Math. Soc. 354 (2002), 2921-2932.
math.GT/0102024.
- With Danny Calegari. Laminations and groups of
homeomorphisms of the circle. Invent. Math. 152 (2003) 149-207. math.GT/0203192.
- With Bill Thurston. The Virtual Haken Conjecture:
Experiments and Examples. Geom. Topol. 7
(2003) 399-441. math.GT/0209214.
Associated software and data.
- With Stavros Garoufalidis. Non-triviality of the A-polynomial for knots in the 3-sphere.
Algebr. Geom. Topology 4 (2004), 1145-1153. math.GT/0405353.
- The Mahler measure of the A-polynomial 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) 3131-3136. math.GR/0412136.
- With Bill Thurston. Finite covers of random
3-manifolds. Invent. Math. 166 (2006) 457-521. math.GT/0502567.
- With Sergei Gukov and Jake Rasmussen. The
superpolynomial for knot homologies. Experimental
Math. 15 (2006), 129-159. math.GT/0505662.
- Volume change under drilling: theory vs. experiment.
Appendix to Agol, Storm, and W. Thurston, Lower bounds on
volumes of hyperbolic Haken 3-manifolds, J. Amer. Math. Soc. 20 (2007), 1053-1077.
math.DG/0506338.
- With Frank Calegari. Automorphic forms and rational
homology 3-spheres, Geom. Topol. 10 (2006) 295-329. math.GT/0508271.
Associated data.
- With Dylan Thurston. A random tunnel number one 3-manifold does not fiber over the circle. Geom. Topol. 10 (2006) 2431-2499. 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) 99-123. math.GT/0607258.
- With Dinakar Ramakrishnan. Increasing the number of
fibered faces of arithmetic hyperbolic 3-manifolds. Amer. J. Math 132 (2010), 53-97. arXiv:0712.3243. Associated software and data.
- With John W. Aaber. Closed surface bundles of least
volume, Algebr. Geom. Topology 10 (2010), 2315-2342. arXiv:1002.3423.
- With Helen Wong. Quantum invariants of random
3-manifolds, Algebr. Geom. Topology 11 (2011) 2191-2205. 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 135-144. arXiv:1012.303.
- With Stavros Garoufalidis. Incompressibility criteria for
spun-normal surfaces,
Trans. Amer. Math. Soc. 64 (2012) 6109-6137. arXiv:1102.4588.
- With Stefan Friedl and Nicholas Jackson. Twisted Alexander
polynomials of hyperbolic knots, Experimental
Math. 21 (2012) 329-352. arXiv:1108.3045.
Associated software and data.
- With Jeff Brock. Injectivity radii of hyperbolic integer
homology 3-spheres, Geom. Topol. 19 (2015), 497-523. arXiv:1304.0391.
- With Neil Hoffman and Joan Licata. Asymmetric hyperbolic
L-spaces, Heegaard genus, and Dehn filling,
Math. Res. Letters, 22 (2015) 1679-1698.
arXiv:1407.7827.
- A diffuse group which is not left-orderable. Appendix to Kionke and
Raimbault, On geometric aspects of diffuse groups,
Documenta Math. 21 (2016) 873-915.
arXiv:1411.6449.
- With Ian Agol. Certifying the Thurston norm via SL(2,
C)-twisted homology, to appear in the Thurston memorial
conference proceedings, Princeton University Press, 23 pages. arXiv:1501.02136.
- A knot without a nonorientable essential spanning
surface, Illinois J. Math. 60 (2016) 179-184.
arXiv:1509.06653.
- With Jeff Brock. Norms on the cohomology of hyperbolic 3-manifolds,
Invent. Math. 210 (2017) 531-558.
arXiv:1510.06292.
- With Marc Culler. Orderability and Dehn filling,
Geom. Topol. 22 (2018) 1405-1457.
arXiv:1602.03793.
- A census of exceptional Dehn fillings,
Characters in low-dimensional topology,
Centre de Recherches Mathématiques Proceedings,
Contemporary Mathematics (to appear), 15 pages.
arXiv:1812.11940.
- Floer homology, group orderability, and taut foliations of hyperbolic 3-manifolds,
Geom. Topol. (to appear), 49 pages.
arXiv:1904.04628.
- With Stavros Garoufalidis and J. Hyam Rubinstein.
Counting essential surfaces in 3-manifolds,
Preprint 2020, 61 pages. arXiv:2007.10053.
- Which small volume hyperbolic 3-manifolds are Haken?
PDF or PostScript (Warwick, 1999).
- Does a random tunnel-number one 3-manifold 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 3-manifolds: the Virtual Haken
Conjecture: PDF (Single), PDF (Double). (Invited address at the AMS meeting in Raleigh, April 2009.)
- Practical solutions to hard problems in 3-dimensional 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. (CBMS-NSF 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 3-spheres.
Complete
video. (Banff, July 2012)
- Surfaces in finite covers of 3-manifolds: the Virtual Haken
Conjecture Complete
video. (GEAR retreat, Urbana, August 2012)
- L-spaces and left-orderability: an experimental survey.
Complete
video. (Banff, April 2013)
- Integer homology 3-spheres with large injectivity radius.
Complete
video. (GTiNY2013, Columbia University, July 2013)
- Practical computation with hyperbolic 3-manifolds. Complete
video. (Thurston Memorial Conference, Cornell, June 2014)
- Computational complexity of problems in 3-dimensional
topology. PDF slides. Complete
video.
(Combinatorial Link Homology Theories, Braids, and Contact Geometry,
ICERM, August 2014)
- What does a random 3-manifold 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 3-manifolds: topology, geometry and arithmetic. Complete video.
(IAS members' seminar, Nov 2015)
- Floer homology, group orders, and taut foliations of hyperbolic
3-manifolds: an experimental survey. Slides. Complete video
(Flows, Foliations and Contact Structures, IAS, Dec 2015)
- Floer homology, group orders, and taut foliations of hyperbolic
3-manifolds: 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 Low-Dimensional 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
20-24. Complete video.
- Floer homology, group orders, and taut foliations of hyperbolic
3-manifolds: an experimental survey. Slides. Complete video
(3-manifold workshops, Newton Institute, Jan 2017)
- Computation of geometric structures, part of a LMS-CMI Research
School at Warwick, September 2017. Course webpage.
- Practical computations with hyperbolic 3-manifolds,
Modularity and 3-manifolds,
ICERM, March 2019: resources and
complete video.
- Computation Demonstration #2,
Perspectives on Dehn Surgery,
ICERM, July 2019: resources and
complete video.
- Illustrating 3-dimensional topology and geometry,
Illustrating Geometry and Topology,
ICERM, September 2019: slides and
complete video.
- Counting incompressible surfaces in three-manifolds, Geometry and Topology Online (GaTO), May 2020.
slides
and complete video.
- Counting incompressible surfaces in three-manifolds, Virtual Seminar on
Geometry and Topology (VISGAT), June 2020.
slides.
- Harmonic 1-forms on hyperbolic 3-manifolds: connections and computations, MSRI, Nov 2020.
slides
and complete video.
Miscellaneous unpublished work
- An interesting relationship between the Jones polynomial and hyperbolic
volume. Web (2000).