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. Published papers use their MR numbers as BibTeX tags. Alternate BibTeX tags for the preprints appear below the entries for those papers.

      1. 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).
      2. 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.
      3. 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.
      4. Transversality in Configuration Spaces and the Square Peg Problem.
        Jason Cantarella, Elizabeth Denne and John McCleary.
      5. 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
      6. The tight knot spectrum in QCD
        Roman Buniy, Jason Cantarella, Thomas Kephart and Eric Rawdon.
        Physical Review D 89 (2014), no. 5, p. 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.
      7. 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 .
      8. 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
      9. 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.
        ANSI C code for generating random polygons according to the methods of this paper is included in our plCurve library.
      10. Ropelength Criticality.
        Jason Cantarella, Joseph H.G. Fu, Rob Kusner, John Sullivan.
        Geometry and Topology 18 (2014), no. 4, p. 1973-2043.
      11. 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
      12. The Shapes of Tight Composite Knots
        Jason Cantarella, Al LaPointe and Eric Rawdon.
        J. Phys A: Math Theor. 45 (2012), p. 1-19
        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
      13. 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
      14. Knot Tightening by Constrained Gradient Descent.
        Ted Ashton, Jason Cantarella, Michael Piatek, and Eric Rawdon.
        Experimental Mathematics 20 (2011), no. 1, p. 57-90.
        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
      15. 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
      16. 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
      17. 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
      18.  Visualizing the tightening of knots
        Jason Cantarella, Michael Piatek, and Eric Rawdon.
        Proceedings of IEEE Visualization 2005, p. 575-582.
      19.  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
        This is the algorithm implemented by the Octrope library.
      20. TSNNLS: A solver for large sparse least squares problems with non-negative variables
        Jason Cantarella and Michael Piatek.
        Unpublished (2004).
        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).
      21. 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.
      22. 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
      23.  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
      24.  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
      25.  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.
      26.  Circles Minimize Most Knot Energies.
        Aaron Abrams, Jason Cantarella, Joe Fu, Mohammad Ghomi, and Ralph Howard.
        Topology 42 (2002) no. 2, p. 381-394.
        This paper was one of the 5 most downloaded articles in the journal Topology during January-August of 2004.
      27. 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.
      28.  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.
      29.  A General Cross-Helicity Formula
        Jason Cantarella.
        Proceedings of the Royal Society, Series A 456 (2000) no. 2003, p. 2771-2779
      30. 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)
      31. 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.
      32.  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)
      33. Topological Structure of Stable Plasma Flows
        Jason Cantarella.
        Ph.D. Thesis, University of Pennsylvania, 1999.
      34.  Tight Knot Values Deviate From Linear Relation
        Jason Cantarella, Robert B. Kusner, and John M. Sullivan.
        Nature 392, March 19, 1998, p. 237.
      35.  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.
      36.  The Principal Eigenvalue of the Curl Operator on the Flat Torus
        Jason Cantarella, Dennis DeTurck, and Herman Gluck.
        Unpublished preprint circa 1996