click on the links to download preprints...

all versions are pre-publication drafts with eventual publication citations as listed

the author gratefully acknowledges the support of the ASDR&E, DARPA, the NSF, the AFOSR, and the ONR; of course, that doesn't mean they endorse what is written. neither does the university of pennsylvania. in fact, i don't think anyone except me and a few coauthors endorse the opinions expressed in these works; and even then, it's not a slam-dunk.



  1. [2023] Z. Cooperband and R. Ghrist, “Towards homological methods in graphic statics”, Proc. IASS 2023, Intl. Assoc. for Shell and Spatial Structures, to appear.
  2. [2023] Y. Baryshnikov and R. Ghrist, “Navigating the negative curvature of Google Maps”, Mathematical Intelligencer, DOI:10.1007/s00283-023-10270-w.
  3. [2022] R. Ghrist, “Network sheaf models for social information systems”, abstract, in Proc. IEEE CIC, Intl. Conf. on Collaboration and Internet Computing.
  4. [2022] H. Riess and R. Ghrist, “Diffusion of Information on Networked Lattices by Gossip”, in Proc. IEEE Conf. on Decision and Control.
  5. [2022] H.-R. Yoon, R. Ghrist, and C. Giusti, “Persistent Extension and Analogous Bars: Data-Induced Relations Between Persistence Barcodes”, J. Appl. Comput. Top., DOI:10.1007/s41468-023-00115-y.
  6. [2021] R. Ghrist and G. Henselman-Petrusek, “Saecular persistence”, preprint.
  7. [2021] A. Parada-Mayorga, H. Riess, A. Ribeiro, and R. Ghrist, “Quiver signal processing”, preprint.
  8. [2021] H. Riess, Y. Kantaros, G. Pappas, and R. Ghrist “Distributed Locally Noninterfering Connectivity via Linear Temporal Logic,” SIAM Conference on Control and Its Applications.
  9. [2020] R. Ghrist and H. Riess, “Cellular sheaves of lattices and the Tarski Laplacian", Homology, Homotopy, & Applications, 24(1) 325-345.
  10. [2020] D. Guralnik and R. Ghrist, “An optimal property of the hyperplane system in a finite cubing”, Autonomous Robotics, 45(2), 665-677. DOI:10.1007/s10514-020-09961-6.
  11. [2020] D. Lee and R. Ghrist, “Path signatures on Lie groups", preprint.
  12. [2020] J. Hansen and R. Ghrist, “Opinion dynamics on discourse sheaves, SIAM J. Appl. Math., 81(5) 2033-2060.
  13. [2020] H.-R. Yoon and R. Ghrist, “Persistence by Parts: Multiscale Feature Detection by Distributed Persistent Homology", preprint.
  14. [2020] A. Speranzon, S. Shivkumar, and R. Ghrist, On Sensor Network Localization Exploiting Topological Constraints, Proc. Amer. Control Conf. [ACC].
  15. [2019] J. Hansen and R. Ghrist, “Towards a spectral theory of cellular sheaves", J. Appl. Comput. Topology, 3(4), 315-358. DOI:10.1007/s41468-019-00038-7.
  16. [2019] A. Sizemore, J. Phillips-Cremins, R. Ghrist, and D. Bassett, "The importance of the whole: topological data analysis for the network neuroscientist", Network Neurosci., 3(3), 656-673.
  17. [2018] Y. Baryshnikov and R. Ghrist, “Minimal unimodal decompositions on trees", preprint, J. Appl. Comput. Topology, 4(), 199-209. DOI:10.1007/s41468-019-00046-7.
  18. [2018] R. Ghrist, R. Levanger, and H. Mai “Persistent homology and Euler integral transforms", J. Appl. Comput. Topology, 2(1-2), 55-60.
  19. [2017] Y. Baryshnikov and R. Ghrist, “Stokes' Theorem, data, and the polar ice caps", Amer. Math. Monthly 125:9, 830-834, 2018.
  20. [2017] R. Ghrist, “Homological Algebra and Data", in The Mathematics of Data, IAS/Park City Mathematics Volume 25, 273-325.
  21. [2016] G. Henselman and R. Ghrist, “Matroid filtrations and computational persistent homology", preprint.
  22. [2016] C. Giusti, R. Ghrist and D. Bassett, “Two's company, three (or more) is a simplex: algebraic-topological tools for understanding higher-order structure in neural data", J. Comput. Neurosci. 41(1), 1-14.
  23. [2015] R. Ghrist and S. Krishnan, “Positive Alexander duality for pursuit and evasion", to appear, SIAM J. Appl. Alg. and Geom.
  24. [2015] S. Bhattachayra and R. Ghrist, “Path homotopy invariants and their application to optimal trajectory planning", to appear, Proc. IMA Conf. on Mathematics & Robotics.
  25. [2014] J. Curry, R. Ghrist, and V. Nanda, “Discrete Morse theory for computing cellular sheaf cohomology" Found. of Comput. Math., DOI 10.1007/s10208-015-9266-8, June 2015.
  26. [2014] C. Jun, S. Bhattachayra, and R. Ghrist (2014), “Pursuit-evasion games on normal distributions", in Proc. IROS, 2014.
  27. [2014] S. Bhattachayra, R. Ghrist, and V. Kumar, “Persistent homology in Z2 coefficients for robot path planning in uncertain environments", IEEE Trans. on Robotics, 31(3), 578 - 590, 2015.
  28. [2013] R. Ghrist, "MOOCs and the Future of Mathematics ", opinion, Notices AMS, Nov. 2013, 1277.
  29. [2013] R. Ghrist and S. Krishnan, "A Topological Max-Flow-Min-Cut Theorem", in Proc. Global Sig. Inf. Proc.
  30. [2012] R. Ghrist, D. Lipsky, J. Derenick, and A. Speranzon, “Topological landmark-based navigation and mapping”, eternal preprint.
  31. [2012] S. Bhattachayra, R. Ghrist, and V. Kumar, “Multi-robot Coverage and Exploration on Riemannian Manifolds with Boundary”, Intl. J. Robotics. Res. 33(1):113-137, 2013.
  32. [2012] Y. Cai and R. Ghrist, “Cyclic network automata and cohomological waves”, in Proc. Info. Proc. in Sensor Networks (IPSN) 2014.
  33. [2012] S. Bhattachayra, D. Lipsky, R. Ghrist, and V. Kumar, “Homology Classes of Cycles in Punctured Euclidean Spaces”, preprint.
  34. [2012] Y. Baryshnikov, R. Ghrist, and M. Wright, “Hadwiger's Theorem for data,” Adv. in Math., 245, 573-586, 2013.
  35. [2011] J. Curry, R. Ghrist, and M. Robinson, “Euler calculus and its applications to signals and sensing,” Proc. Sympos. Appl. Math., AMS, 2012.
  36. [2011] M. Robinson and R. Ghrist, “Topological localization via signals of opportunity,” IEEE Trans. Signal Processing, 60(5), 2362-2373, 2012.
  37. [2011] Y. Baryshnikov and R. Ghrist, “Unimodal Category and Topological Statistics,” Proc. NOLTA, 2011.
  38. [2011] R. Ghrist and M. Robinson, “Euler-Bessel and Euler-Fourier Transforms,” Inverse Problems, 27(12), 124006, 2011.
  39. [2011] R. Ghrist and Y. Hiraoka, “Applications of sheaf cohomology and exact sequences to network coding,” in Proc. NOLTA, 2011.
  40. [2011] Y. Baryshnikov, R. Ghrist, and D. Lipsky, “Inversion of Euler integral transforms with applications to sensor data,” Inverse Problems 27(12), 124001, 2011.
  41. [2011] P. Dlotko, M. Juda, M. Mrozek, and R. Ghrist, “Distributed computation of coverage in sensor networks by homological methods”, Applicable Algebra in Engineering, Communication and Computing, 23 (1-2), 29-58, 2012.
  42. [2011] M. Katsev, A. Yershova, B. Tovar, R. Ghrist, and S. LaValle, “Mapping and Pursuit-Evasion Strategies For a Simple Wall-Following Robot,” IEEE Transactions on Robotics, 27(1). 113-128, 2011.
  43. [2010] R. Ghrist, “Applied Algebraic Topology & Sensor Networks,” a manu-script text. (caveat! file>50megs!)
  44. [2010] Y. Baryshnikov and R. Ghrist, “Euler integration for definable functions,” Proc. National Acad. Sci., 107(21), May 25, 9525-9530, 2010. Published version available at journal.
  45. [2010] R. Ghrist, J.B. Van den Berg, R. Vandervorst, and W. Wojcik, “Braid Floer homology,” J. Diff. Eqns, 259(5), 1663-1721, 2015.
  46. [2010] S. Alexander, R. Bishop, and R. Ghrist, "Total curvature and simple pursuit on domains of curvature bounded above," Geom. Dedicata, 149(1), 275-290, 2010.
  47. [2010] E. Chambers, V. de Silva, J. Erickson, and R. Ghrist, “Rips complexes for planar point sets," Disc. Comput. Geom., 44(1), 75-90.
  48. [2010] R. Ghrist, “Configuration spaces, braids, and robotics,” Lecture Note Series, Inst. Math. Sci., NUS, vol. 19, World Scientific, 263-304.
  49. [2009] S. Alexander, R. Bishop, and R. Ghrist, "Capture pursuit games on unbounded domains," Ensiegn. Math., 55, 103-125.
  50. [2009] Y. Baryshnikov and R. Ghrist, "Target enumeration via Euler characteristic integrals," SIAM J. Appl. Math., 70(3), 825-844.
  51. [2009] R. Ghrist and R. Vandervorst, “Braids and parabolic scalar PDEs,'' Transactions Amer. Math. Soc., 361, 2755-2788.
  52. [2008] R. Ghrist, “Barcodes: The persistent topology of data,'' Bull. Amer. Math. Soc., 45(1) 61-75. Published article available from the AMS.
  53. [2008] R. Ghrist, “Three examples of applied and computational homology," Nieuw Archief voor Wiskunde 5/9(2).
  54. [2008] Y. Baryshnikov and R. Ghrist, “Target enumeration via integration over planar sensor networks,” in Proc. Robotics: Science & Systems.
  55. [2008] J. Jung and R. Ghrist, “Pareto optimal multi-robot coordination with acceleration constraints,” in Proc. Intl. Conf. Robotics & Automation.
  56. [2007] R. Ghrist, “Winding numbers for networks with weak angular data,” in Topology and Robotics, Contemporary Mathematics, AMS.
  57. [2007] V. de Silva and R. Ghrist, “Homological sensor networks,” Notices Amer. Math. Soc., 54(1), 10-17. Published article available from the AMS.
  58. [2007] V. de Silva and R. Ghrist, “Coverage in sensor networks via persistent homology,” Alg. & Geom. Topology, 7, 339-–358.
  59. [2007] R. Ghrist, “On the contact geometry and topology of ideal fluids,” Handbook of Mathematical Fluid Dynamics, Vol. IV., 1-38.
  60. [2007] R. Ghrist and V. Peterson, “The geometry and topology of reconfiguration,” Adv. Appl. Math., 38, 302–323.
  61. [2006] V. de Silva and R. Ghrist, “Coordinate-free coverage in sensor networks with controlled boundaries,” Intl. J. Robotics Research, 25(12), 1205-1222.
  62. [2006] R. Ghrist and S. LaValle, “Nonpositive curvature and Pareto optimal motion planning,” SIAM J. Control & Opt., 45(5), 1697-1713.
  63. [2006] E. Klavins, R. Ghrist, and D. Lipsky, “The graph grammatical approach to self-organizing robotic systems,” IEEE Trans. Automatic Controls, 51(6), 949-962.
  64. [2006] R. Ghrist and R. Komendarczyk, “Overtwisted energy-minimizing curl eigenfields,” Nonlinearity, 19(1), 41-52.
  65. [2005] R. Ghrist, J. O'Kane, and S. LaValle, “Computing Pareto-optimal coordinations on roadmaps,” Intl. J. Robotics Research, 12(11), 997-1010.
  66. [2005] J. Etnyre and R. Ghrist, “Generic hydrodynamic instability for curl eigenfields,” SIAM J. Appl. Dynamical Systems, 4(2), 377-390.
  67. [2006] R. Ghrist “Braids and differential equations,'' in Proc. International Congress of Mathematicians, vol. III, 1-26.
  68. [2006] R. Ghrist, D. Lipsky, S. Poduri, and G. Sukhatme, “Node isolation in coordinate-free networks,'' in Proc. Workshop on Algorithmic Foundations of Robotics.
  69. [2006] S. Alexander, R. Bishop, and R. Ghrist, “Pursuit and evasion on nonconvex domains of arbitrary dimensions,'' in Proc. Robotics: Science & Systems.
  70. [2005] A. Yershova, B. Tovar, R. Ghrist, and S. LaValle, “Bitbots: Simple robots solving complex tasks,'' in Proc. AAAI.
  71. [2005] V. de Silva, R. Ghrist, and A. Muhammad, “Blind swarms for coverage in 2-d,'' in Proc. Robotics, Systems and Science.
  72. [2005] R. Ghrist and A. Muhammad, “Coverage and hole detection in sensor networks via homology,'' in Proc. Information Processing in Sensor Networks.
  73. [2004] A. Abrams and R. Ghrist, “State complexes for metamorphic robots,” Intl. J. Robotics Research, 23(7,8), 809-824.
  74. [2004] R. Ghrist and E. Kin, “Flowlines transervse to knot and link fibrations,” Pacific J. Math., 217(1), 61-86.
  75. [2004] R. Ghrist, J. O'Kane, and S. LaValle, “Pareto optimal coordination on roadmaps,'' in Proc. Workshop on Algorithmic Foundations of Robotics, 2004.
  76. [2004] R. Ghrist, and D. Lipsky, “Grammatical self-assembly for planar tiles,'' in Proc. Intl. Conf. on MEMS, Nano, and Smart Systems.
  77. [2004] E. Klavins, R. Ghrist, and D. Lipsky, “Graph grammars for self-assembling robot systems,'' in Proc. Intl. Conf. on Robotics & Automation.
  78. [2003] R. Ghrist, J.B.Van den Berg, and R.C. Vandervorst, “Morse theory on braids with applications to Lagrangian systems,” Invent. Math., 152(2), 369-432.
  79. [2002] J. Etnyre and R. Ghrist, “Contact topology and hydrodynamics II: Solid tori,” Ergod. Thy. & Dyn. Sys., 22(3), 819-833.
  80. [2002] J. Etnyre and R. Ghrist, “Contact topology and Anosov flows,” Top. & its Appl., 124 (2), 211-219.
  81. [2002] R. Ghrist and D. Koditschek, “Safe cooperative robot dynamics on graphs,” SIAM J. Cont. & Opt., 40(5), 1556-1575.
  82. [2002] A. Abrams and R. Ghrist, “Finding topology in a factory: configuration space,” Amer. Math. Monthly, 109, 140-150.
  83. [2002] R. Ghrist, “Shape complexes for metamorphic robots,'' in Algorithmic Foundations of Robotics V, J. Boissonnat et al. eds., STAR 7, Springer, 185-201.
  84. [2002] R. Ghrist and R. Komendarczyk, “Topological features of inviscid flows,” in Introduction to the Geometry and Topology of Fluid Flows, NATO-ASI Series II, vol. 47, Kluwer Press, 183-202.
  85. [2001] J. Etnyre and R. Ghrist, “An index for closed orbits in Beltrami fields,” Physica D, 159(3-4), 180-189.
  86. [2001] R. Ghrist, “Steady nonintegrable high-dimensional fluids,” Lett. Math. Phys., 55(3), 193-204.
  87. [2001] R. Ghrist, “Configuration spaces of graphs and robotics,” in Braids, Links, and Mapping Class Groups: the Proceedings of Joan Birman's 70th Birthday, AMS/IP Studies in Mathematics, vol. 24, 29-40.
  88. [2000] R. Ghrist, J.B.Vandenberg, and R.C. Vandervorst, “Closed characteristics of fourth-order twist systems via braids,” C. R. Acad. Sci. Paris Ser. I, 331, 861- 865.
  89. [2000] J. Etnyre and R. Ghrist,) “Contact topology and hydrodynamics III: knotted orbits,” Trans. Amer. Math. Soc., 352, 5781-5794.
  90. [2000] R. Ghrist, “Resonant gluing bifurcations,” Intl. J. Bifurcation and Chaos, 10(9), 2141-2160.
  91. [2000] J. Etnyre and R. Ghrist, “Contact topology and hydrodynamics I: Beltrami fields and the Seifert Conjecture,” Nonlinearity 13, 441-458.
  92. [2000] R. Ghrist, E. Klavins, and D. Koditschek, “Cyclic regulation of patterns,'' Proc. Workshop on Algorithmic Foundations of Robotics, B. Donald, K. Lynch, and D. Rus, eds., 205-220.
  93. [1999] J. Etnyre and R. Ghrist, “Plane field flows,” Comment. Math. Helv., 74, 507-529.
  94. [1999] J. Etnyre and R. Ghrist, “Construction of tight 3-manifolds via dynamics,” Proc. Amer. Math. Soc., 127, 3697-3706.
  95. [1999] J. Etnyre and R. Ghrist, “Stratified integrals and unknots in inviscid flows,” Cont. Math., 246,99-112.
  96. [1999] R. Ghrist and D. Koditschek, “Safe Cooperative Robot Dynamics on Graphs,'' in Hybrid Systems and AI: Modeling, Analysis and Control of Discrete and Continuous Systems, AAAI, SS-99-05, 65-70.
  97. [1998] R. Ghrist and T. Young, “From Morse-Smale to all links,” Nonlinearity, 11, 1111-1125.
  98. [1998] R. Ghrist, “Chaotic knots and wild dynamics”, Chaos, Solitons, and Fractals, 9(4/5), 583-598.
  99. [1997] R. Ghrist, P. Holmes, and M. Sullivan, Knots and Links in Three-Dimensional Flows, Lecture Notes in Mathematics, Volume 1654, Springer-Verlag.
  100. [1997] R. Ghrist, “Accumulations of infinite links,” Topology and its Applications, 81, 171-184.
  101. [1997] R. Ghrist, “Branched 2-manifolds supporting all links,” Topology, 36(2), 423-438.
  102. [1996] R. Ghrist and P. Holmes, “An ODE whose solutions contain all knots,” Intl. J. Bifurcation and Chaos, 6(5), 779-800.
  103. [1995] R. Ghrist, “Flows on S3 supporting all links as orbits,” Electronic Research Announcements of the AMS, 1(2), 91-97.
  104. [1994] R. Ghrist and P. Holmes, “Knotting within the gluing bifurcation,'' in IUTAM Symposium on Nonlinearity and Chaos in Engineering Dynamics, J. M. T. Thompson and S. R. Bishop, Ed., John Wiley Press, 299-315.
  105. [1993] R. Ghrist and P. Holmes, “Knots and orbit genealogies in three dimensional flows,'' in Bifurcations and Periodic Orbits of Vector Fields, NATO ASI Series C, Volume 408, Kluwer Academic Publishers, 185-239.