Publications and Preprints

All of my papers and preprints are stored on, 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

  1. 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.
  2. Examples of non-trivial roots of unity at ideal points of hyperbolic 3-manifolds. Topology 38 (1999), 457 - 465. math.GT/9801064.
  3. Cyclic surgery, degrees of maps of character curves, and volume rigidity for hyperbolic manifolds. Invent. Math. 136 (1999) 3, 623-657. math.GT/9802022.
  4. A table of boundary slopes of Montesinos knots. Topology, 40 (2001) 2, 309-315. math.GT/9901120. Associated software.
  5. Alexander and Thurston norms of fibered 3-manifolds. Pacific J. Math. 200 (2001), 43-58. math.GT/9908050.
  6. With Danny Calegari. Commensurability of 1-cusped hyperbolic 3-manifolds. Trans. Amer. Math. Soc. 354 (2002), 2921-2932. math.GT/0102024.
  7. With Danny Calegari. Laminations and groups of homeomorphisms of the circle. Invent. Math. 152 (2003) 149-207. math.GT/0203192.
  8. With Bill Thurston. The Virtual Haken Conjecture: Experiments and Examples. Geom. Topol. 7 (2003) 399-441. math.GT/0209214. Associated software and data.
  9. 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.
  10. 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.
  11. 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.
  12. With Bill Thurston. Finite covers of random 3-manifolds. Invent. Math. 166 (2006) 457-521. math.GT/0502567.
  13. With Sergei Gukov and Jake Rasmussen. The superpolynomial for knot homologies. Experimental Math. 15 (2006), 129-159. math.GT/0505662.
  14. 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.
  15. With Frank Calegari. Automorphic forms and rational homology 3-spheres, Geom. Topol. 10 (2006) 295-329. math.GT/0508271. Associated data.
  16. 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.
  17. 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.
  18. 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.
  19. With John W. Aaber. Closed surface bundles of least volume, Algebr. Geom. Topology 10 (2010), 2315-2342. arXiv:1002.3423.
  20. With Helen Wong. Quantum invariants of random 3-manifolds, Algebr. Geom. Topology 11 (2011) 2191-2205. arXiv:1009.1653.
  21. 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.
  22. With Stavros Garoufalidis. Incompressibility criteria for spun-normal surfaces, Trans. Amer. Math. Soc. 64 (2012) 6109-6137. arXiv:1102.4588.
  23. 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.
  24. With Jeff Brock. Injectivity radii of hyperbolic integer homology 3-spheres, Geom. Topol. 19 (2015), 497-523. arXiv:1304.0391.
  25. 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.
  26. 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.
  27. 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), 1--20, Princeton Univ. Press. arXiv:1501.02136.
  28. A knot without a nonorientable essential spanning surface, Illinois J. Math. 60 (2016) 179-184. arXiv:1509.06653.
  29. With Jeff Brock. Norms on the cohomology of hyperbolic 3-manifolds, Invent. Math. 210 (2017) 531-558. arXiv:1510.06292.
  30. With Marc Culler. Orderability and Dehn filling, Geom. Topol. 22 (2018) 1405-1457. arXiv:1602.03793.
  31. A census of exceptional Dehn fillings, Characters in low-dimensional topology, Contemp. Math. 760 (2020) 143-155. arXiv:1812.11940.
  32. Floer homology, group orderability, and taut foliations of hyperbolic 3-manifolds, Geom. Topol. 24 (2020), 2075-2125. arXiv:1904.04628.
  33. With Stavros Garoufalidis and J. Hyam Rubinstein. Counting essential surfaces in 3-manifolds, Invent. Math. 228 (2022), 717-775. arXiv:2007.10053.
  34. 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.
  35. 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 37:1-37:24. arXiv:2112.03251.
  36. With Jacob Rasmussen. A unified Casson-Lin invariant for the real forms of SL(2). Preprint, 147 pages. arXiv:2209.03382.

Slides and video recordings of talks

  1. Which small volume hyperbolic 3-manifolds are Haken? PDF or PostScript (Warwick, 1999).
  2. Does a random tunnel-number one 3-manifold fiber over the circle? PDF or PostScript (Treiste 2005).
  3. Mathematical Truths: Experiment, Proof, and Understanding. PDF (From a public lecture at Bowdoin Collge in 2007).
  4. 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.)
  5. Practical solutions to hard problems in 3-dimensional topology: PDF (Single), PDF (Double) (Hamilton Geometry and Topology Workshop, September 2009.)
  6. Hyperbolically twisted Alexander polynomials of knots: PDF (Single), PDF (Double) (Jacofest, June 2010)
  7. The Least Spanning Area of a Knot and the Optimal Homologous Chain Problem: PDF (Single), PDF (Double) (SoCG, Paris, June 2011)
  8. The Least Spanning Area of a Knot and the Optimal Homologous Chain Problem: PDF (Single), PDF (Double) (Hyamfest, July 2011)
  9. Hyperbolically twisted Alexander polynomials of knots : PDF (Single), PDF (Double). Complete video. (CBMS-NSF Conference, NYC, August 2011)
  10. Hyperbolically twisted Alexander polynomials of knots : PDF (Single), PDF (Double). (Gauge Theory Seminar, Harvard, April 2012)
  11. Hyperbolic geometry of integer homology 3-spheres. Complete video. (Banff, July 2012)
  12. Surfaces in finite covers of 3-manifolds: the Virtual Haken Conjecture Complete video. (GEAR retreat, Urbana, August 2012)
  13. L-spaces and left-orderability: an experimental survey. Complete video. (Banff, April 2013)
  14. Integer homology 3-spheres with large injectivity radius. Complete video. (GTiNY2013, Columbia University, July 2013)
  15. Practical computation with hyperbolic 3-manifolds. Complete video. (Thurston Memorial Conference, Cornell, June 2014)
  16. Computational complexity of problems in 3-dimensional topology. PDF slides. Complete video. (Combinatorial Link Homology Theories, Braids, and Contact Geometry, ICERM, August 2014)
  17. What does a random 3-manifold look like? PDF slides. (Combinatorial Link Homology Theories, Braids, and Contact Geometry, ICERM, August 2014)
  18. Random knots: a preliminary report. PDF slides. (Various conferences, Fall 2014)
  19. Certifying the Thurston norm via twisted homology. Complete video. (GGD/GEAR Seminar, January 2015)
  20. A tale of two norms. Complete video. (New Developments in TQFT, CQM, Aarhus, July 2015)
  21. A tale of two norms. Complete video. (GGD/GEAR Seminar, August 2015)
  22. Fun with finite covers of 3-manifolds: topology, geometry and arithmetic. Complete video. (IAS members' seminar, Nov 2015)
  23. 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)
  24. 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)
  25. Orderability and Dehn filling. Complete video. (Geometric Group Theory and Low-Dimensional Topology, ICTP, Trieste, June 2016)
  26. 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.
  27. Floer homology, group orders, and taut foliations of hyperbolic 3-manifolds: an experimental survey. Slides. Complete video (3-manifold workshops, Newton Institute, Jan 2017)
  28. Computation of geometric structures, part of a LMS-CMI Research School at Warwick, September 2017. Course webpage.
  29. Practical computations with hyperbolic 3-manifolds, Modularity and 3-manifolds, ICERM, March 2019: resources and complete video.
  30. Computation Demonstration #2, Perspectives on Dehn Surgery, ICERM, July 2019: resources and complete video.
  31. Illustrating 3-dimensional topology and geometry, Illustrating Geometry and Topology, ICERM, September 2019: slides and complete video.
  32. Counting incompressible surfaces in three-manifolds, Geometry and Topology Online (GaTO), May 2020. slides and complete video.
  33. Counting incompressible surfaces in three-manifolds, Virtual Seminar on Geometry and Topology (VISGAT), June 2020. slides.
  34. Harmonic 1-forms on hyperbolic 3-manifolds: connections and computations, MSRI, Nov 2020. slides and complete video.
  35. Counting incompressible surfaces in three-manifolds, CMO, June 2021. slides and and complete video.

Miscellaneous unpublished work

  1. An interesting relationship between the Jones polynomial and hyperbolic volume. Web (2000).

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