Preprints and Publications:

This page contains links to my research publications and preprints, for experts in the field. For an overview of my research, including the types of problems I study, and some videos, please see my Research Info page.

Note most papers and preprints are also available on the ArXiv.

Preprints
  1. Alternating links on nonorientable surfaces and Klein-bottly alternating links
    With Lecheng Su
    Preprint (15 pages):[pdf]. arXiv:2412.07133.

  2. Triangulations of the 3-sphere with knotted edge
    With Dionne Ibarra, Daniel Mathews, and Jonathan Spreer
    Preprint (19 pages):[pdf]. arXiv:2411.18938.

  3. Volume bounds for hyperbolic rod complements in the 3-torus
    With Norman Do and Connie On Yu Hui
    Preprint (19 pages):[pdf]. arXiv:2409.02357.

  4. Excluding cosmetic surgeries on hyperbolic 3-manifolds
    With David Futer and Saul Schleimer
    Preprint (29 pages):[pdf]. arXiv:2403.10448.

  5. Polynomial bounds for surfaces in cusped 3-manifolds
    With Anastasiia Tsvietkova
    Preprint (26 pages):[pdf]. arXiv:2311.08567.

  6. Geometry of fully augmented links in doubled 3-manifolds
    With Corbin Reid and John Stewart
    Preprint (15 page):[pdf]. arXiv:2310.18976.

  7. Standard position for surfaces in link complements in arbitrary 3-manifolds
    With Anastasiia Tsvietkova
    Preprint (39 pages): [pdf]. arXiv:2205.06368.

Publications

  1. Hyperbolic and satellite Lorenz links obtained by twisting
    With Thiago de Paiva
    Michigan Mathematical Journal, to appear
    Preprint (21 pages): [pdf]. arXiv:2301.01934.

  2. A symplectic basis for 3-manifold triangulations
    With Daniel V. Mathews
    Communications in Analysis and Geometry, to appear
    Preprint version (45 pages): [pdf]. arXiv:2208.06969.

  3. A-polynomials, Ptolemy equations and Dehn filling
    With Josh Howie and Dan Mathews
    Algebraic and Geometric Topology, to appear
    Preprint version (46 pages): [pdf]. ArXiv.

  4. Large volume fibred knots of fixed genus
    With Kenneth L. Baker, David Futer and Saul Schleimer
    Mathematical Research Letters, to appear.
    Preprint version (6 pages): [pdf]. Arxiv.

  5. Alternating links on surfaces and volume bounds
    With Effie Kalfagianni
    Communications in Analysis and Geometry, Vol. 32 (2024), no. 1, 119-151.
    Preprint version (24 pages): [pdf]. ArXiv.

  6. The triangulation complexity of elliptic and sol 3-manifolds
    With Marc Lackenby
    Mathematische Annalen, Vol. 290 (2024), no. 2, 1623-1667.
    Preprint version (41 pages): [pdf]. Arxiv.

  7. The triangulation complexity of fibred 3-manifolds
    With Marc Lackenby
    Geometry & Topology, Vol. 28 (2024), no. 4, 1727-1828.
    Preprint (77 pages): [pdf]. ArXiv.

  8. On the geometry of rod packings in the 3-torus
    With Connie On Yu Hui
    Bulletin of the London Mathematical Society, Vol. 56 (2024), No. 4, 1291-1309
    Preprint version (20 pages): [pdf]. Arxiv.

  9. Arithmetic modular links
    With Tali Pinsky and Jose Andres Rodriguez-Migueles
    Pacific Journal of Mathematics, Vol. 327 (2023), No. 2, 337-358.
    Preprint version (18 pages): [pdf]. ArXiv.

  10. A-Polynomials of fillings of the Whitehead sister
    With Joshua Howie, Daniel Mathews, and Em Thompson
    International Journal of Mathematics, Vol. 34 (2023), No. 13, 2350085.
    Preprint version (18 pages):[pdf]. ArXiv.

  11. Satellites and Lorenz knots
    With Thiago de Paiva
    International Mathematics Research Notices (IMRN), Vol. 2023 (2023), no. 19, 16540-16573.
    Preprint version (24 pages): [pdf]. ArXiv.

  12. Constructing knots with specified geometric limits
    With Urs Fuchs, John Stewart
    Pacific Journal of Mathematics, Vol. 324 (2023), No. 1, 111-142.
    Preprint version (27 pages): [pdf]. ArXiv.

  13. Geometric triangulations and highly twisted links
    With Sophie Ham
    Algebraic and Geometric Topology, Vol. 23 (2023), 1399-1462.
    Preprint version (40 pages): [pdf]. ArXiv.

  14. Effective drilling and filling of tame hyperbolic 3-manifolds
    With David Futer and Saul Schleimer
    Commentarii Mathematici Helvetici, Vol. 97 (2022), No. 3, 457-512.
    Preprint version (36 pages):[pdf]. ArXiv.

  15. Effective bilipschitz bounds on drilling and filling
    With David Futer and Saul Schleimer
    Geometry & Topology, Volume 26 (2022), No. 3, 1077-1188.
    Preprint version (72 pages): [pdf]. ArXiv.

  16. Right-angled polyhedra and alternating knots
    With Abhijit Champanerkar and Ilya Kofman
    Algebraic & Geometric Topology, Volume 22 (2022), No. 2, pp 739-784.
    Preprint version (32 pages): [pdf]. ArXiv.

  17. State graphs and fibered state surfaces
    With Darlan Girao
    Algebraic and Geometric Topology, Volume 20 (2020), No. 2, pp 987-1014.
    Preprint version (20 pages): [pdf]. ArXiv.

  18. Geometry of alternating links on surfaces
    With Josh Howie
    Transactions of the American Mathematical Society, Volume 373 (2020), No. 4, pp 2349-2397.
    Preprint version (44 pages): [pdf]. ArXiv.

  19. Treewidth, crushing, and hyperbolic volume
    With Clement Maria
    Algebraic and Geometric Topology, Volume 19 (2019), No. 5, pp 2625-2652.
    Preprint version (20 pages): [pdf]. ArXiv.

  20. Effective distance between nested Margulis tubes
    With David Futer and Saul Schleimer
    Transactions of the American Mathematical Society, Volume 372 (2019), No. 6, pp 4211-4237.
    Preprint version (25 pages): [pdf]. ArXiv.

  21. On the tree-width of knot diagrams
    With Arnaud de Mesmay, Saul Schleimer, and Eric Sedgwick
    Journal of Computational Geometry, Volume 10 (2019), No. 1, pp 164-180.
    Preprint (14 pages): [pdf]. ArXiv.

  22. A survey of hyperbolic knot theory (Book chapter)
    With David Futer and Efstratia Kalfagianni
    Knots, Low-Dimensional Topology and Applications, Springer Proceedings in Mathematics & Statistics, Volume 284 (2019), pp 1-30.
    Preprint version (20 pages): [pdf]. ArXiv.

  23. Geometry of biperiodic alternating links
    With Abhijit Champanerkar and Ilya Kofman
    Journal of the London Mathematical Society, Vol. 99 (2019), No. 3, pp. 807-830.
    Preprint version (25 pages): [pdf]. ArXiv.

  24. Cusp shape and tunnel number
    With Vinh Dang
    Proceedings of the American Mathematical Society, Vol. 147 (2019), pp 1351-1366.
    Preprint version (15 pages): [pdf]. ArXiv.

  25. Spacious knots
    With Autumn Kent
    Mathematical Research Letters, Vol. 25 (2018), No. 2, pp 581-595.
    Preprint version (10 pages): [pdf]. ArXiv.

  26. Geometry of planar surfaces and exceptional fillings
    With Neil Hoffman.
    Bulletin of the London Mathematical Society, Vol. 49 (2017), No. 2, pp. 185-201.
    Preprint version (17 pages): [pdf]. ArXiv.

  27. Independence of volume and genus g bridge numbers
    With Alex Zupan
    Proceedings of the American Mathematical Society, Vol. 145 (2017), No. 4, 1805-1818.
    Preprint version (14 pages): [pdf]. ArXiv.

  28. Geometrically and diagrammatically maximal knots
    With Abhijit Champanerkar and Ilya Kofman.
    Journal of the London Mathematical Society, Vol. 94 (2016), No. 3, 883-908.
    Preprint version (26 pages): [pdf]. ArXiv.

  29. Volume bounds for weaving knots
    With Abhijit Champanerkar and Ilya Kofman.
    Algebraic and Geoemtric Topology, Vol. 16 (2016), No. 6, 3301-3323.
    Preprint version (17 pages): [pdf]. ArXiv.

  30. Essential twisted surfaces in alternating link complements
    With Marc Lackenby.
    Algebraic and Geometric Topology, Vol. 16 (2016), No. 6, 3209-3270.
    Preprint version (51 pages): [pdf]. ArXiv.

  31. Cusp volumes of alternating knots
    With Marc Lackenby.
    Geometry and Topology, Vol. 20 (2016), No. 4, 2053-2078.
    Preprint version (21 pages): [pdf]. ArXiv.

  32. Bi-twist manifolds and two-bridge knots
    With J. W. Cannon, W. J. Floyd, L. Lambert, W. R. Parry
    Pacific Journal of Mathematics, Vol. 284 (2016), No. 1, 1-39.
    Preprint version (28 pages): [pdf]. ArXiv.

  33. Density spectra for knots
    With Abhijit Champanerkar and Ilya Kofman.
    Journal of Knot Theory and its Ramifications, Vol. 25 (2016), no. 3, 164001, 11 pages.
    Preprint (8 pages): [pdf]. ArXiv.

  34. Volumes of Montesinos links
    With Kathleen Finlinson.
    Pacific Journal of Mathematics. Vol. 282 (2016), no. 1, 63-105.
    Preprint version (41 pages): [pdf]. ArXiv.

  35. Hyperbolic semi-adequate links
    With David Futer and Efstratia Kalfagianni.
    Communications in Analysis and Geometry. Vol. 23 (2015), no. 5, 993-1030.
    Preprint version (25 pages): [pdf]. ArXiv.

  36. Volume and geometry of homogeneously adequate knots
    With Paige Bartholomew, Shane McQuarrie, and Kai Weser.
    Journal of Knot Theory and its Ramifications, Vol. 24 (2015), no. 8, 1550044, 29 pages.
    Preprint version (26 pages):[pdf]. ArXiv.

  37. Geodesics and compression bodies
    With Marc Lackenby.
    Experimental Mathematics, Vol. 23 (2014), no. 2, 218-240.
    Preprint (31 pages): [pdf]. ArXiv.

  38. Geodesic systems of tunnels in hyperbolic 3-manifolds
    With Stephan D. Burton.
    Algebraic and Geometric Topology, Vol. 14 (2014), no. 2, 925-952.
    Preprint version (19 pages): [pdf]. ArXiv.

  39. Quasifuchsian state surfaces
    With David Futer and Efstratia Kalfagianni.
    Transactions of the American Mathematical Society, Vol. 366 (2014), no. 8, 4323-4343.
    Preprint version (21 pages): [pdf]. ArXiv.

  40. Jones polynomials, volume, and essential knot surfaces: a survey
    With David Futer and Efstratia Kalfagianni.
    Proceedings of Knots in Poland III, Banach Center Publications, Vol. 100 (2014), pages 51-77.
    Preprint version (27 pages): [pdf]. ArXiv.

  41. Dehn filling and the geometry of unknotting tunnels
    With Daryl Cooper and David Futer.
    Geometry and Topology, Vol. 17 (2013), no. 3, 1815-1876.
    Preprint version (45 pages): [pdf]. ArXiv.

  42. Explicit Dehn filling and Heegaard splittings
    With David Futer.
    Communications in Analysis and Geometry, Vol. 21 (2013), no. 3, 625-650.
    Preprint version (17 pages): [pdf]. ArXiv.

  43. Guts of surfaces and the colored Jones polynomial
    With David Futer and Efstratia Kalfagianni.
    Lecture Notes in Mathematics, Vol. 2069, Springer, Berlin, 2013.
    Preprint version (179 pages): [pdf]. ArXiv.

  44. Volumes of chain links
    With James Kaiser and Clint Rollins.
    Journal of Knot Theory and Its Ramifications, Vol. 21 (2012), No. 11, 1250115, 17 pp.
    Preprint version (14 pages): [pdf]. ArXiv.
    Computational code and data available here.

                  

  45. Volume bounds for generalized twisted torus links
    With Abhijit Champanerkar, David Futer, Ilya Kofman, and Walter Neumann.
    Mathematical Research Letters, Vol. 18 (2011), no. 6, 1097--1120.
    Preprint version (21 pages): [pdf]. ArXiv.

  46. An introduction to fully augmented links,
    Interactions between hyperbolic geometry, quantum topology, and number theory, Contemporary Mathematics, Vol 541, (2011), pp. 205--220.
    Preprint version (16 pages): [pdf].

  47. Slopes and colored Jones polynomials of adequate knots
    With D. Futer and E. Kalfagianni.
    Proceedings of the American Mathematical Society, Vol. 139 (2011), no. 5, pp. 1889-1896.
    Preprint version (7 pages): [pdf]. ArXiv.

  48. Geometric limits of knot complements
    With Juan Souto.
    Journal of Topology, Vol 3 (2010), no. 4, pp. 759-785.
    Preprint version (37 pages): [pdf]. ArXiv.

  49. Cusp areas of Farey manifolds and applications to knot theory
    With D. Futer and E. Kalfagianni.
    International Mathematics Research Notices, Vol 2010 (2010), no. 23, pp. 4434-4497.
    Preprint version (44 pages): [pdf]. ArXiv.

  50. On multiply twisted knots that are Seifert fibered or toroidal
    Communications in Analysis and Geometry. Vol 18 (2010), no. 2, pp. 219-256.
    Preprint version (32 pages): [pdf]. ArXiv.

  51. On diagrammatic bounds of knot volumes and spectral invariants
    With David Futer and Efstratia Kalfagianni.
    Geometriae Dedicata, Vol. 147 (2010), no. 1, pp. 115-130.
    Preprint version (16 pages): [pdf]. ArXiv.

  52. Hyperbolic geometry of multiply twisted knots
    Communications in Analysis and Geometry. Vol 18 (2010), no. 1, pp. 101-120.
    Preprint version (17 pages): [pdf]. ArXiv.

  53. The length of unknotting tunnels
    With Daryl Cooper and Marc Lackenby.
    Algebraic & Geometric Topology, Vol. 10 (2010) pp. 637-661.
    Preprint version (20 pages): [pdf]. ArXiv.

  54. Symmetric links and Conway sums: volume and Jones polynomial.
    With D. Futer and E. Kalfagianni.
    Mathematical Research Letters, Vol. 16 (2009), no. 2, pp. 233-253.
    Preprint version (18 pages): [pdf], ArXiv.

  55. Cusp shapes under cone deformation.
    Journal of Differential Geometry, Vol. 80 (2008), no. 3, pp. 453-500.
    Preprint version (46 pages): [pdf], ArXiv.

  56. Slope lengths and generalized augmented links.
    Communications in Analysis and Geometry, Vol. 16 (2008), no. 4, pp. 883-905.
    Preprint version (20 pages): [pdf], ArXiv.

  57. Dehn filling, volume, and the Jones polynomial.
    With D. Futer and E. Kalfagianni.
    Journal of Differential Geometry, Vol. 78 (2008), no. 3, pp. 429-464.
    Preprint version (34 pages): [pdf], ArXiv.

  58. Links with no exceptional surgeries.
    With David Futer.
    Commentarii Mathematici Helvetici, Vol. 8 (2007), no. 3, pp. 629-664.
    Preprint version (29 pages): [pdf], ArXiv.

  59. Volumes of highly twisted knots and links.
    Algebraic & Geometric Topology, Vol. 7 (2007), pp. 93-108.
    Preprint version (14 pages): [pdf], ArXiv.

Purgatory

  1. Diagram uniqueness for highly twisted plats, with Yoav Moriah
    Unfortunately there is a gap in the argument, in Section 3. The same error affects both papers. We thought we had a fix, but after some time we realise the fix is harder than expected. Thus these two papers are now in purgatory.

    For now, the old versions are available here and on the ArXiv (withdrawn).
    Original (27 pages): [pdf]. ArXiv.
    Even plats (20 pages): [pdf]. ArXiv.

Publications In Computer Science (as Jessica Shepherd)
  1. Riloff, E. and Shepherd, J., (1999) "A Corpus-Based Bootstrapping Algorithm for Semi-Automated Semantic Lexicon Construction", Journal of Natural Language Engineering , 1999, Vol. 5, No. 2, pp. 147-156.

  2. Riloff, E. and Shepherd, J. (1997) "A Corpus-Based Approach for Building Semantic Lexicons", Proceedings of the Second Conference on Empirical Methods in Natural Language Processing (EMNLP-2).