robert ghrist home page

robert ghrist home page
robert ghrist
prof-g
cv
math
papers
EAT
CALC
ART
press
bio
papers & preprints
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.
CHRONOLOGICAL LISTING
[2025] R. Ghrist and Z. Cooperband,
“Obstructions to Reality: Torsors & Visual Paradox”
[2025] H.-R. Yoon, G. Henselman-Petrusek, Y. Yu, R. Ghrist, S. LaVere Smith, and C. Giusti,
“Tracking the topology of neural manifolds across populations”
Proc. Nat. Acad. Sci.
2024, 121(46), e2407997121.
[2025] Z. Cooperband and R. Ghrist,
“Unified Origami Kinematics via Cosheaf Homology”
[2025] R. Ghrist, M. Lopez, P. Randall North, and H. Riess
“Categorical Diffusion of Weighted Lattices”
[2025] R. Ghrist, J. Gould, M. Lopez, and H. Riess
“Clearing Sections of Lattice Liability Networks”
[2024] R. Ghrist, J. Gould, M. Lopez, and H. Riess
“Lattice-Valued Bottleneck Duality”
[2023] Z. Cooperband, R. Ghrist, and J. Hansen,
“A Cosheaf Theory of Reciprocal Figures: Planar and Higher Genus Graphic Statics”
[2023] H. Riess, G. Henselman-Petrusek, M. C. Munger, R. Ghrist, Z. I. Bell, and M. M. Zavlanos,
“Network Preference Dynamics using Lattice Theory”
[2023] Z. Cooperband and R. Ghrist,
“Towards homological methods in graphic statics”
Proc. IASS 2023, Intl. Assoc. for Shell and Spatial Structures
, to appear.
[2023] Y. Baryshnikov and R. Ghrist,
“Navigating the negative curvature of Google Maps”
Mathematical Intelligencer
, DOI:10.1007/s00283-023-10270-w.
[2022] R. Ghrist,
“Network sheaf models for social information systems”
, abstract, in
Proc. IEEE CIC, Intl. Conf. on Collaboration and Internet Computing
[2022] H. Riess and R. Ghrist,
“Diffusion of Information on Networked Lattices by Gossip”
, in
Proc. IEEE Conf. on Decision and Control.
[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.
[2021] R. Ghrist and G. Henselman-Petrusek,
“Saecular persistence”
[2021] A. Parada-Mayorga, H. Riess, A. Ribeiro, and R. Ghrist,
“Quiver signal processing”
[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
[2020] R. Ghrist and H. Riess, “
Cellular sheaves of lattices and the Tarski Laplacian
",
Homology, Homotopy, & Applications
, 24(1) 325-345.
[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.
[2020] D. Lee and R. Ghrist, “
Path signatures on Lie groups
", preprint.
[2020] J. Hansen and R. Ghrist, “
Opinion dynamics on discourse sheaves
SIAM J. Appl. Math.
, 81(5) 2033-2060.
[2020] H.-R. Yoon and R. Ghrist, “
Persistence by Parts: Multiscale Feature Detection by Distributed Persistent Homology
", preprint.
[2020] A. Speranzon, S. Shivkumar, and R. Ghrist,
On Sensor Network Localization Exploiting Topological Constraints
Proc. Amer. Control Conf.
[ACC].
[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.
[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.
[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.
[2018] R. Ghrist, R. Levanger, and H. Mai “
Persistent homology and Euler integral transforms
",
J. Appl. Comput. Topology
, 2(1-2), 55-60.
[2017] Y. Baryshnikov and R. Ghrist, “
Stokes' Theorem, data, and the polar ice caps
",
Amer. Math. Monthly
125:9, 830-834, 2018.
[2017] R. Ghrist, “
Homological Algebra and Data
", in
The Mathematics of Data
, IAS/Park City Mathematics Volume 25, 273-325.
[2016] G. Henselman and R. Ghrist, “
Matroid filtrations and computational persistent homology
", preprint.
[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.
[2015] R. Ghrist and S. Krishnan, “
Positive Alexander duality for pursuit and evasion
", to appear,
SIAM J. Appl. Alg. and Geom.
[2015] S. Bhattachayra and R. Ghrist, “
Path homotopy invariants and their application to optimal trajectory planning
", to appear,
Proc. IMA Conf. on Mathematics & Robotics
[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.
[2014] C. Jun, S. Bhattachayra, and R. Ghrist (2014), “
Pursuit-evasion games on normal distributions
", in
Proc. IROS
, 2014.
[2014] S. Bhattachayra, R. Ghrist, and V. Kumar, “
Persistent homology in Z
coefficients for robot path planning in uncertain environments
",
IEEE Trans. on Robotics
, 31(3), 578 - 590, 2015.
[2013] R. Ghrist, "
MOOCs and the Future of Mathematics
", opinion,
Notices AMS
, Nov. 2013, 1277.
[2013] R. Ghrist and S. Krishnan, "
A Topological Max-Flow-Min-Cut Theorem
", in
Proc. Global Sig. Inf. Proc.
[2012] R. Ghrist, D. Lipsky, J. Derenick, and A. Speranzon, “
Topological landmark-based navigation and mapping
”, eternal preprint.
[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.
[2012] Y. Cai and R. Ghrist, “
Cyclic network automata and cohomological waves
”, in
Proc. Info. Proc. in Sensor Networks (IPSN) 2014
[2012] S. Bhattachayra, D. Lipsky, R. Ghrist, and V. Kumar, “
Homology Classes of Cycles in Punctured Euclidean Spaces
”, preprint.
[2012] Y. Baryshnikov, R. Ghrist, and M. Wright, “
Hadwiger's Theorem for data
,”
Adv. in Math.
, 245, 573-586, 2013.
[2011] J. Curry, R. Ghrist, and M. Robinson, “
Euler calculus and its applications to signals and sensing
,”
Proc. Sympos. Appl. Math.
, AMS, 2012.
[2011] M. Robinson and R. Ghrist, “
Topological localization via signals of opportunity
,”
IEEE Trans. Signal Processing
, 60(5), 2362-2373, 2012.
[2011] Y. Baryshnikov and R. Ghrist, “
Unimodal Category and Topological Statistics
,”
Proc. NOLTA
, 2011.
[2011] R. Ghrist and M. Robinson, “
Euler-Bessel and Euler-Fourier Transforms
,”
Inverse Problems,
27(12), 124006, 2011.
[2011] R. Ghrist and Y. Hiraoka, “
Applications of sheaf cohomology and exact sequences to network coding
,” in
Proc. NOLTA
, 2011.
[2011] Y. Baryshnikov, R. Ghrist, and D. Lipsky, “
Inversion of Euler integral transforms with applications to sensor data
,”
Inverse Problems
27(12), 124001, 2011.
[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.
[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.
[2010] R. Ghrist, “
Applied Algebraic Topology & Sensor Networks
,” a manu-script text. (caveat! file>50megs!)
[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.
[2010] R. Ghrist, J.B. Van den Berg, R. Vandervorst, and W. Wojcik, “
Braid Floer homology
,”
J. Diff. Eqns
, 259(5), 1663-1721, 2015.
[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.
[2010] E. Chambers, V. de Silva, J. Erickson, and R. Ghrist, “
Rips complexes for planar point sets
,"
Disc. Comput. Geom.
, 44(1), 75-90.
[2010] R. Ghrist, “
Configuration spaces, braids, and robotics
,”
Lecture Note Series, Inst. Math. Sci., NUS
, vol. 19, World Scientific, 263-304.
[2009] S. Alexander, R. Bishop, and R. Ghrist, "
Capture pursuit games on unbounded domains
,"
Ensiegn. Math.
, 55, 103-125.
[2009] Y. Baryshnikov and R. Ghrist, "
Target enumeration via Euler characteristic integrals
,"
SIAM J. Appl. Math.
, 70(3), 825-844.
[2009] R. Ghrist and R. Vandervorst, “
Braids and parabolic scalar PDEs
,''
Transactions Amer. Math. Soc.
, 361, 2755-2788.
[2008] R. Ghrist, “
Barcodes: The persistent topology of data
,''
Bull. Amer. Math. Soc.
, 45(1) 61-75.
Published article
available from the AMS.
[2008] R. Ghrist, “
Three examples of applied and computational homology
,"
Nieuw Archief voor Wiskunde
5/9(2).
[2008] Y. Baryshnikov and R. Ghrist, “
Target enumeration via integration over planar sensor networks
,” in
Proc. Robotics: Science & Systems.
[2008] J. Jung and R. Ghrist, “
Pareto optimal multi-robot coordination with acceleration constraints
,” in
Proc. Intl. Conf. Robotics & Automation.
[2007] R. Ghrist, “
Winding numbers for networks with weak angular data
,” in
Topology and Robotics
, Contemporary Mathematics, AMS.
[2007] V. de Silva and R. Ghrist, “
Homological sensor networks
,”
Notices Amer. Math. Soc.
, 54(1), 10-17.
Published article
available from the AMS.
[2007] V. de Silva and R. Ghrist, “
Coverage in sensor networks via persistent homology
,”
Alg. & Geom. Topology
, 7, 339-–358.
[2007] R. Ghrist, “
On the contact geometry and topology of ideal fluids
,”
Handbook of Mathematical Fluid Dynamics
, Vol. IV., 1-38.
[2007] R. Ghrist and V. Peterson, “
The geometry and topology of reconfiguration
,”
Adv. Appl. Math.
, 38, 302–323.
[2006] V. de Silva and R. Ghrist, “
Coordinate-free coverage in sensor networks with controlled boundaries
,”
Intl. J. Robotics Research
, 25(12), 1205-1222.
[2006] R. Ghrist and S. LaValle, “
Nonpositive curvature and Pareto optimal motion planning
,”
SIAM J. Control & Opt.
, 45(5), 1697-1713.
[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.
[2006] R. Ghrist and R. Komendarczyk, “
Overtwisted energy-minimizing curl eigenfields
,”
Nonlinearity
, 19(1), 41-52.
[2005] R. Ghrist, J. O'Kane, and S. LaValle, “
Computing Pareto-optimal coordinations on roadmaps
,”
Intl. J. Robotics Research
, 12(11), 997-1010.
[2005] J. Etnyre and R. Ghrist, “
Generic hydrodynamic instability for curl eigenfields
,”
SIAM J. Appl. Dynamical Systems
, 4(2), 377-390.
[2006] R. Ghrist “
Braids and differential equations
,'' in Proc. International Congress of Mathematicians, vol. III, 1-26.
[2006] R. Ghrist, D. Lipsky, S. Poduri, and G. Sukhatme, “
Node isolation in coordinate-free networks
,'' in Proc. Workshop on Algorithmic Foundations of Robotics.
[2006] S. Alexander, R. Bishop, and R. Ghrist, “
Pursuit and evasion on nonconvex domains of arbitrary dimensions
,'' in Proc. Robotics: Science & Systems.
[2005] A. Yershova, B. Tovar, R. Ghrist, and S. LaValle, “
Bitbots: Simple robots solving complex tasks
,'' in Proc. AAAI.
[2005] V. de Silva, R. Ghrist, and A. Muhammad, “
Blind swarms for coverage in 2-d
,'' in Proc. Robotics, Systems and Science.
[2005] R. Ghrist and A. Muhammad, “
Coverage and hole detection in sensor networks via homology
,'' in Proc. Information Processing in Sensor Networks.
[2004] A. Abrams and R. Ghrist, “
State complexes for metamorphic robots
,”
Intl. J. Robotics Research
, 23(7,8), 809-824.
[2004] R. Ghrist and E. Kin, “
Flowlines transervse to knot and link fibrations
,”
Pacific J. Math.
, 217(1), 61-86.
[2004] R. Ghrist, J. O'Kane, and S. LaValle, “
Pareto optimal coordination on roadmaps
,'' in
Proc. Workshop on Algorithmic Foundations of Robotics
, 2004.
[2004] R. Ghrist, and D. Lipsky, “
Grammatical self-assembly for planar tiles
,'' in
Proc. Intl. Conf. on MEMS, Nano, and Smart Systems
[2004] E. Klavins, R. Ghrist, and D. Lipsky, “
Graph grammars for self-assembling robot systems
,'' in
Proc. Intl. Conf. on Robotics & Automation
[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.
[2002] J. Etnyre and R. Ghrist, “
Contact topology and hydrodynamics II: Solid tori
,”
Ergod. Thy. & Dyn. Sys.
, 22(3), 819-833.
[2002] J. Etnyre and R. Ghrist, “
Contact topology and Anosov flows
,”
Top. & its Appl.
, 124 (2), 211-219.
[2002] R. Ghrist and D. Koditschek, “
Safe cooperative robot dynamics on graphs
,”
SIAM J. Cont. & Opt.
, 40(5), 1556-1575.
[2002] A. Abrams and R. Ghrist, “
Finding topology in a factory: configuration space
,”
Amer. Math. Monthly
, 109, 140-150.
[2002] R. Ghrist, “
Shape complexes for metamorphic robots
,'' in
Algorithmic Foundations of Robotics
V, J. Boissonnat et al. eds., STAR 7, Springer, 185-201.
[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.
[2001] J. Etnyre and R. Ghrist, “
An index for closed orbits in Beltrami fields
,”
Physica D
, 159(3-4), 180-189.
[2001] R. Ghrist, “
Steady nonintegrable high-dimensional fluids
,”
Lett. Math. Phys.
, 55(3), 193-204.
[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.
[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.
[2000] J. Etnyre and R. Ghrist,) “
Contact topology and hydrodynamics III: knotted orbits
,”
Trans. Amer. Math. Soc.
, 352, 5781-5794.
[2000] R. Ghrist, “
Resonant gluing bifurcations
,”
Intl. J. Bifurcation and Chaos
, 10(9), 2141-2160.
[2000] J. Etnyre and R. Ghrist, “
Contact topology and hydrodynamics I: Beltrami fields and the Seifert Conjecture
,”
Nonlinearity
13, 441-458.
[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.
[1999] J. Etnyre and R. Ghrist, “
Plane field flows
,”
Comment. Math. Helv.
, 74, 507-529.
[1999] J. Etnyre and R. Ghrist, “
Construction of tight 3-manifolds via dynamics
,”
Proc. Amer. Math. Soc.
, 127, 3697-3706.
[1999] J. Etnyre and R. Ghrist, “
Stratified integrals and unknots in inviscid flows
,”
Cont. Math
., 246,99-112.
[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.
[1998] R. Ghrist and T. Young, “
From Morse-Smale to all links
,”
Nonlinearity
, 11, 1111-1125.
[1998] R. Ghrist, “
Chaotic knots and wild dynamics
”,
Chaos, Solitons, and Fractals
, 9(4/5), 583-598.
[1997] R. Ghrist, P. Holmes, and M. Sullivan,
Knots and Links in Three-Dimensional Flows
, Lecture Notes in Mathematics, Volume 1654, Springer-Verlag.
[1997] R. Ghrist, “
Accumulations of infinite links
,”
Topology and its Applications
, 81, 171-184.
[1997] R. Ghrist, “
Branched 2-manifolds supporting all links
,”
Topology
, 36(2), 423-438.
[1996] R. Ghrist and P. Holmes, “
An ODE whose solutions contain all knots
,”
Intl. J. Bifurcation and Chaos
, 6(5), 779-800.
[1995] R. Ghrist, “
Flows on S
supporting all links as orbits
,”
Electronic Research Announcements of the AMS
, 1(2), 91-97.
[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.
[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.
website © 2014-2020 robert ghrist