Papers

To obtain a copy of any of the papers listed below, click on the title of the paper. The preprints should be cited by arXiv number (as they are all also available from the arXiv). You can get citation information for these papers from my Google author profile if you’re interested. The BibTeX citation information for all the papers is collected in cantarella.bib.

  1. On the average squared radius of gyration of a family of embeddings of subdivision graphs.
    Jason Cantarella, Henrik Schumacher, and Clayton Shonkwiler.
    arXiv preprint 2409.18767
  2. CoBarS: Fast reweighted sampling for polygons in any dimension.
    Jason Cantarella and Henrik Schumacher.
    SIAM Journal on Applied Algebra and Geometry 8 (2024), 756-781.
    C++ implementation on GitHub
    Mathematica interface to library on GitHub
  3. A faster direct sampling algorithm for equilateral polygons and the probability of unknotting.
    Jason Cantarella, Henrik Schumacher, and Clayton Shonkwiler.
    Journal of Physics A 57 (2024) p. 285205
  4. Random graph embeddings with general edge potentials.
    Jason Cantarella, Tetsuo Deguchi, Clayton Shonkwiler and Erica Uehara.
    arXiv preprint 2205.09049
  5. Exact Evaluation of the Mean Square Radius of Gyration for Gaussian Topological Polymer Chains.
    Jason Cantarella, Tetsuo Deguchi, Clayton Shonkwiler and Erica Uehara.
    in Topological Polymer Chemistry, Tezuka and Deguchi, eds, Springer, 2021.
  6. Families of similar simplices inscribed in most smoothly embedded spheres.
    Jason Cantarella, Elizabeth Denne, and John McCleary.
    Forum of Mathematics, Sigma 10 (2022) , e101.
  7. Square-like quadrilaterals inscribed in embedded space curves.
    Jason Cantarella, Elizabeth Denne, and John McCleary.
    arXiv preprint 2103.13848 
  8.  Configuration Spaces, Multijet Transversality, and the Square-Peg Problem.
    Jason Cantarella, Elizabeth Denne, and John McCleary.
    Illinois Journal of Mathematics 66 (2022), no. 3, p. 385–420.
  9. Performance of the Uniform Closure Method for open knotting as a Bayes-type classifier.
    Emily Tibor, Elizabeth Annoni, Erin Brine-Doyle, Nicole Kumerow, Madeline Shogren, Jason Cantarella, Clayton Shonkwiler, and Eric Rawdon.
    arXiv preprint 2011.08984 
  10. Radius of Gyration, Contraction Factors, and Subdivisions of Topological Polymers.
    Jason Cantarella, Tetsuo Deguchi, Clayton Shonkwiler, and Erica Uehara.
    Journal of Physics A 55 (2022), no. 47, p. 475202.
  11. Computing the Conformal Barycenter.
    Jason Cantarella and Henrik Schumacher.
    SIAM Journal on Applied Algebra and Geometry 6 (2022), no. 3, p. 503-530.
    Mathematica implementation on GitHub.
  12. Gaussian Random Embeddings of Multigraphs.
    Jason Cantarella, Tetsuo Deguchi, Clayton Shonkwiler, and Erica Uehara.
    arXiv preprint 2001.11709
  13. Open and closed random walks with fixed edgelengths in R^d
    Jason Cantarella, Kyle Chapman, Philipp Reiter, and Clayton Shonkwiler.
    Journal of Physics A 51 (2018), no. 43, p. 434002
  14. Random Triangles and Polygons in the Plane.
    Jason Cantarella, Thomas Needham, and Clayton Shonkwiler.
    American Mathematical Monthly 126 (2019), no. 2, p.113-134
  15. Knot Fertility and Lineage.
    Jason Cantarella, Allison Henrich, Elsa Magness, Oliver O’Keefe, Kayla Perez, Eric Rawdon, Brianna Zimmer.
    Journal of Knot Theory and Its Ramifications 26 (2017), no. 13, p. 1750093
  16. Knot Probabilities in Random Diagrams.
    Jason Cantarella, Harrison Chapman and Matt Mastin.
    Journal of Physics A 49 (2016), p. 405001
    This paper comes with a tabulation of knot diagrams up to 10 crossings (including pictures) as supplementary data (53M).
  17. A Fast Direct Sampling Algorithm for Equilateral Closed Polygons.
    Jason Cantarella, Bertrand Duplantier, Clayton Shonkwiler and Erica Uehara.
    Journal of Physics A 49 (2016), no. 27, p. 275205.
    This paper was one of the highlights of the year for 2016 in Mathematical Physics.
  18. Rigid Origami Vertices: Conditions and Forcing Sets.
    Zachary Abel, Jason Cantarella, Erik D. Demaine, David Eppstein, Thomas C. Hull, Jason S. Ku, Robert J. Lang, Tomohiro Tachi.
    Journal of Computational Geometry 7 (2016), no. 1, p. 171-184.
  19. Transversality in Configuration Spaces and the Square Peg Problem.
    Jason Cantarella, Elizabeth Denne and John McCleary.
    arXiv:1402.6174
  20. The Symplectic Geometry of Closed Equilateral Random Walks in 3-space
    Jason Cantarella and Clayton Shonkwiler.
    Annals of Applied Probability 26 (2016), no. 1, p. 549-596
    A 30-minute talk on this paper for physicists and biologists
    Slides from the talk
  21. The tight knot spectrum in QCD. 
    Roman Buniy, Jason Cantarella, Thomas Kephart and Eric Rawdon.
    Physical Review D 89 (2014), no. 5, p. 054513
    PhysRevD.89.054513
    This paper comes with a data set of tight knot and link vertex coordinates and summary data (including prime and composite knots and links and curvature information) and a low-resolution archive of tight knot and link vertex coordinates.
  22. The Expected Total Curvature of Random Polygons.
    Jason Cantarella, Alexander Y Grosberg, Robert B Kusner and Clayton Shonkwiler.
    American Journal of Mathematics 137, (2015), no. 2, p. 411-438 .
    arXiv:1210.6537.
    2012arXiv1206.3161C
  23. Symmetric Criticality for Tight Knots.
    Jason Cantarella, Jennifer Ellis, Joseph H.G. Fu and Matt Mastin.
    Journal of Knot Theory and its Ramifications 23 (2014), 1450008-1-17
    arXiv:1208.3879.
    doi:10.1142/S0218216514500084
  24. Probability Theory of Random Polygons from the Quaternionic Viewpoint.
    Jason Cantarella, Tetsuo Deguchi and Clayton Shonkwiler.
    Communications on Pure and Applied Mathematics 67 (2014), no. 10, p. 1658-1699.
    CPA:CPA21480
    ANSI C code for generating random polygons according to the methods of this paper is included in our plCurve library.
  25. Ropelength Criticality.
    Jason Cantarella, Joseph H.G. Fu, Rob Kusner, John Sullivan.
    Geometry and Topology 18 (2014), no. 4, p. 1973-2043.
    gtropelengthcriticality
  26. The 27 possible intrinsic symmetry groups of 2-component links.
    Jason Cantarella, James Cornish, Matt Mastin and Jason Parsley.
    Symmetry 4 (2012), no. 1, p. 129-142
    sym4010129
  27. The Shapes of Tight Composite Knots
    Jason Cantarella, Al LaPointe and Eric Rawdon.
    J. Phys A: Math Theor. 45 (2012), p. 1-19
    arXiv:1110.3262
    1751-8121-45-22-225202
    This paper comes with several data files: tight knot and link vertex coordinates (including prime and composite knots and links and curvature information) and a low-resolution version of tight knot and link vertex coordinates. This data was generated with support from NSF grants 1115722 and 0810415 (to Rawdon). This paper was the source of the cover image of the Journal of Physics A the month it was publishedJphysAcover
  28. Intrinsic Symmetry Groups of Links with 8 and fewer crossings
    Michael Berglund, Jason Cantarella, Meredith Perrie Casey,
    Ellie Dannenberg, Whitney George, Aja Johnson, Amelia Kelly,
    Al LaPointe, Matt Mastin, Jason Parsley, Jacob Rooney and Rachel Whitaker.
    Symmetry 4 (2012), no. 1, p. 143-207.
    arXiv:1010.3234 sym4010143
  29. Knot Tightening by Constrained Gradient Descent.
    Ted Ashton, Jason Cantarella, Michael Piatek, and Eric Rawdon.
    Experimental Mathematics 20 (2011), no. 1, p. 57-90.
    arXiv:1002.1723
    acprtightening
    See also Self contact sets for 50 Tightly Knotted and Linked Tubes, which is an early version of this paper. The data sets corresponding to this paper are the Atlas of Tight Knots and Links, the archive of Tight Knot and Link Vertex Coordinates and a text file summary of ropelengths for knots and links. This paper was the source of the cover image for Experimental Math when published:
    Experimental Mathematics Cover
  30. A new cohomological formula for helicity in $\R^{2k+1}$ reveals the effect of a diffeomorphism on helicity.
    Jason Cantarella and Jason Parsley.
    Journal of Geometry and Physics 60 (2010), p. 1127-1155.
    arxiv: math.GT/09031465
    Cantarella20101127
  31. Criticality for the Gehring Link Problem.
    Jason Cantarella, Joseph H.G. Fu, Rob Kusner, John M. Sullivan, and Nancy Wrinkle.
    Geometry and Topology 10 (2006), p. 2055-2116.
    arXiv: math.DG/0402212
    MR2284052
  32. On Comparing the Writhe of a Smooth Curve to the Writhe of an Inscribed Polygon.
    Jason Cantarella.
    SIAM Journal of Numerical Analysis 42 (2005) no. 4, p. 1846-1861.
    arXiv: math.DG/0202236
    MR2139226
  33.  Visualizing the tightening of knots
    Jason Cantarella, Michael Piatek, and Eric Rawdon.
    Proceedings of IEEE Visualization 2005, p. 575-582.
    cprvis
  34.  A fast octree-based algorithm for computing ropelength
    Ted Ashton and Jason Cantarella
    In Physical and Numerical Models in Knot Theory
    and their Application to the Life Sciences,
    World Scientific Press (2005), p. 323-341
    arxiv
    MR2197947
    This is the algorithm implemented by the Octrope library.
  35. TSNNLS: A solver for large sparse least squares problems with non-negative variables
    Jason Cantarella and Michael Piatek.
    Unpublished (2004).
    arxiv:cs.MS/0408029
    tsnnls
    This unpublished manuscript describes the algorithm implemented in our open-source TSNNLS library. The library is used around the world for solving sparse constrained least squares problems of moderate size (matrices dimensions of a few thousand by a few thousand). TSNNLS was very fast for its day, but it is not an actively updated package and it is probably somewhat behind the times at this point. If you want to do more general or much larger problems of this type, I’d look at the COIN-OR project (specifically IpOPT).
  36. An Energy-Driven Approach to Linkage Unfolding.
    Jason Cantarella, Erik Demaine, Hayley Iben and James O’Brien.
    SCG ’04: Proceedings of the twentieth annual symposium on Computational geometry, p. 134-143
    Abstract (not posted) in Proceedings of the 12th Annual DIMACS Fall Workshop
    on Computational Geometry, Piscataway, New Jersey, November 14-15, 2002.
    James O’Brien and Hayley Iben prepared some cool movies and wrote a nice Java applet to demonstrate some of the results from this paper. Here are some updated video files showing the unfolding
  37. Upper Bounds for Ropelength as a function of Crossing Number.
    Jason Cantarella, X.W. Faber, and Chad A. Mullikin.
    Topology and its Applications 135 (2003), no. 1-3, p. 253-264.
    arXiv: math.GT/0210245
    Cantarella2004253
  38.  The Second Hull of a Knotted Curve.
    Jason Cantarella, Greg Kuperberg, Robert B. Kusner, and John M. Sullivan.
    American Journal of Mathematics 125 (2003) no. 6, p. 1335-1348.
    arXiv: math.GT/0204106
    MR2018663
  39.  Vector Calculus and the Topology of Domains in 3-Space.
    Jason Cantarella, Dennis DeTurck, and Herman Gluck.
    American Mathematical Monthly 109 (2002) no. 5. p. 409-442
    MR2003c:53023
  40.  On the Minimum Ropelength of Knots and Links.
    Jason Cantarella, Robert B. Kusner, and John M. Sullivan.
    Inventiones Mathematicae 150 (2002) no. 2, p. 257-286.
    MR2003h:58014
  41.  Circles Minimize Most Knot Energies.
    Aaron Abrams, Jason Cantarella, Joe Fu, Mohammad Ghomi, and Ralph Howard.
    Topology 42 (2002) no. 2, p. 381-394.
    MR2004f:58014
    This paper was one of the 5 most downloaded articles in the journal Topology during January-August of 2004.
  42. The Biot-Savart operator for application to knot theory, fluid dynamics, and plasma physics
    Jason Cantarella, Dennis DeTurck, and Herman Gluck.
    Journal of Mathematical Physics 42 (2001), no. 2, p. 876-905.
    MR2002e:78002
  43.  Isoperimetric problems for the helicity of vector fields and the Biot-Savart and curl operators
    Jason Cantarella, Dennis DeTurck, Herman Gluck, and Mikhail Teytel.
    Journal of Mathematical Physics 41 (2000), no. 8, p. 5615-5641.
    MR2001f:78010
  44.  A General Cross-Helicity Formula
    Jason Cantarella.
    Proceedings of the Royal Society, Series A 456 (2000) no. 2003, p. 2771-2779
    MR2002f:53002
  45. Upper Bounds for the Writhing of Knots and the Helicity of Vector Fields
    Jason Cantarella, Dennis DeTurck, and Herman Gluck.
    Proceedings of the Conference in Honor of the 70th Birthday of Joan Birman
    Jane Gilman, Xiao-Song Lin, William Menasco (eds)
    International Press, AMS/IP Series on Advanced Mathematics (2000)
    MR2003j:58018
  46. Eigenvalues and Eigenfields of the Biot-Savart and Curl Operators on Spherically Symmetric Domains
    Jason Cantarella, Dennis DeTurck, Herman Gluck, and Misha Teytel.
    Physics of Plasmas 7(7), 2000. pp.2766-2775.
    MR2001b:76094
  47.  Influence of Geometry and Topology on Helicity
    Jason Cantarella, Dennis DeTurck, Herman Gluck, and Misha Teytel.
    In Magnetic Helicity in Space and Laboratory Plasmas,
    Michael Brown, Richard Canfield and Alexei Pevtsov (eds),
    Geophysical Monographs 111, American Geophysical Union. (1999)
    influence
  48. Topological Structure of Stable Plasma Flows
    Jason Cantarella.
    Ph.D. Thesis, University of Pennsylvania, 1999.
    cantarellathesis
  49.  Tight Knot Values Deviate From Linear Relation
    Jason Cantarella, Robert B. Kusner, and John M. Sullivan.
    Nature 392, March 19, 1998, p. 237.
    cksnature
  50.  Nontrivial Embeddings of Polygonal Intervals and Unknots in 3-Space
    Jason Cantarella and Heather Johnston.
    Journal of Knot Theory and its Ramifications, Vol. 7, No. 8 (1998) p. 1027-1039.
    MR99m:57002
  51.  The Principal Eigenvalue of the Curl Operator on the Flat Torus
    Jason Cantarella, Dennis DeTurck, and Herman Gluck.
    Unpublished preprint circa 1996

These works were produced under the “general obligation to produce scholarly and creative works” and copyright is retained by the authors or assigned to publishers per individual agreements.