topological methods in applied mathematics

preprints

The author gratefully acknowledges the support of DARPA, the National Science Foundation, and the ONR; specifically:

ONR - N000140810668 "Algebraic-Topological Structures for Hidden Modes"
DARPA - HR0011-07-1-0002 "SToMP: Sensor Topology & Minimal Planning"
NSF MPSA-MCS - 0528086 "Fundamental Geodesic Problems in Computational Topology"
DARPA - HR0011-05-1-0008 "Topological Tools for Sensors and Systems"
NSF DMS - 0337713 "PECASE: Topological Methods in Applied Mathematics"
NSF INT   - 0089631 "East Asia / Pacific: Topological methods in Nonlinear Dynamics"
NSF DMS - 9971629 "Topological Techniques in Hydrodynamics"
NSF DMS - 9508846 "Knots and Links in Three-Dimensional Flows"

 

 

robert ghrist

Y. Baryshnikov and R. Ghrist, Euler integration over definable functions, (posted 6/09), draft of a work-in-progress.

Y. Baryshnikov and R. Ghrist, Target enumeration via Euler characteristic integrals, (posted 1/07, updated 3/07, then 6/08), preprint. To appear in SIAM J. Appl. Math.  More in progress...

Y. Baryshnikov and R. Ghrist, Target enumeration via integration over planar
sensor networks
, (posted 6/08), preprint. In Proc. Robotics Systems & Science, 2008.

E. Chambers, V. de Silva, J. Erickson, and R. Ghrist, Rips complexes of planar point sets, (posted 12/07), preprint, to appear in Disc. Comput. Geom.

V. de Silva and R. Ghrist, Coordinate-free coverage in sensor networks with controlled boundaries via homology, (posted 8/05, revised, 1/06), Intl. J. Robotics Research. 25(12), 1205--1222, 2006.

V. de Silva and R. Ghrist, Homological sensor networks, (posted 11/05),  Notices American Mathematical Society, 54(1), 10--17, 2007.

V. de Silva and R. Ghrist, Coverage in sensor networks via persistent homology, (posted 11/05), Alg. & Geom. Topology, 7, 339-358, 2007.

R. Ghrist, Winding numbers for networks with weak angular data , (posted 11/06), to appear in Topology and Robotics, M. Farber, R. Ghrist, M. Berger, and D. Koditschek eds., Contemporary Mathematics 438, AMS, 1-18, 2007.

R. Ghrist, D. Lipsky, S. Poduri, and G. Sukhatme, Surrounding nodes in coordinate-free networks, (posted 6/06), Proc. Workshop in Algorithmic Foundations of Robotics, 2006.

V. de Silva, R. Ghrist and A. Muhammad, Blind swarms for coverage in 2-d, (posted 1/05), in Proc. Robotics Systems & Science, 2005.

All papers on this site are non-official, .pdf preprint versions, distinct from the published version

S. Alexander, R. Bishop, and R. Ghrist, Capture pursuit games on unbounded domains, (posted 1/2008) to appear, Enseign. Math.

J. Jung and R. Ghrist,  Pareto optimal multi-robot coordination with acceleration constraints, (posted 12/07), Proc. ICRA 2008.

R. Ghrist and V. Peterson, The geometry and topology of reconfiguration, (posted 5/05), Advances in Applied Mathematics 38, 302--323, 2007.

S. Alexander, R. Bishop, and R. Ghrist, Pursuit and evasion in arbitrary dimensions, (posted 1/06, revised 5/06),  Proc. Robotics Systems & Science, 2006.

E. Klavins, R. Ghrist, and D. Lipsky, A grammatical approach to self-organizing robotic systems, (posted 7/05, revised 12/05), IEEE Trans. Aut. Controls, 51(6) 949-962, 2006.

R. Ghrist, J. O'Kane,and S. LaValle, Computing Pareto optimal coordinations on roadmaps, (posted 1/05), Intl. J. Robotics Research, 12(11), 997--1010, 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, (posted 1/05), in Proc. Robotics Systems & Science, 2005.

R. Ghrist and S. LaValle, Nonpositive curvature and Pareto-optimal coordination of robots, (posted 9/04, revised 2/06),  SIAM J. Control & Optimization, 45(5), 1697--1713, 2006.

E. Klavins, R. Ghrist, and D. Lipsky, Graph grammars for self-assembling robotic systems, (posted 11/02), in Proc. Intl. Conf. Robotics and Automation 2004

R. Ghrist, J. OKane, and S. LaValle, Pareto-optimal coordination on roadmaps, (posted 2/04), in Proc. Workshop in Algorithmic Foundations of Robotics 2004.

A. Abrams and R. Ghrist, State complexes for metamorphic robot systems, (posted 4/03, revised 8/03), preprint.  Intl. J. of Robotics Research, 23(7,8), 809--824, 2004. 

R. Ghrist, Shape complexes for metamorphic robot systems, (posted 7/02, revised 11/02), in Proc. Workshop in Algorithmic Foundations of Robotics 2002.

R. Ghrist and D. Koditschek,  Safe, cooperative robot dynamics on graphs , (posted 2/00),  SIAM J. Control & Optimization, 40(5), 1556-1575, 2002.

A. Abrams and R. Ghrist,  Finding topology in a factory: configuration spaces,  (posted 9/00),   American Mathematics Monthly, 109, 140-150, February 2002. 

R. Ghrist, Configuration spaces and braid groups on graphs in robotics, (posted, 10/98). In Braids, Links, and Mapping Class Groups: the Proceedings of Joan Birmans 70th Birthday, AMS/IP Studies in Mathematics volume 24, 29-40, 2001.  

R. Ghrist and D. Koditschek, Safe cooperative robotic motions via dynamics on graphs, Eighth Intl. Symp. on Robotic Research, Y. Nakayama, ed., Springer-Verlag, 81-92, 1998.

R. Ghrist, On the contact topology and geometry of ideal fluids, (posted 12/05), Handbook of Mathematical Fluid Dynamics vol. IV, 1-38, 2007.

R. Ghrist and R. Komendarczyk, Overtwisted energy-minimizing curl eigenfields, (posted 12/04), preprint version.  Nonlinearity, 19(1), 41--52, 2006.

J. Etnyre and R. Ghrist, Generic hydrodynamic instability for curl eigenfields, (posted 6/03), SIAM J. Appl. Dynamical Systems, 22(3), 819-833, 2005.

J. Etnyre and R. Ghrist, An index for closed orbits of Beltrami fields, (posted 1/01), Physica D 159, 180-189, 2001. 

R. Ghrist, Steady nonintegrable high-dimensional fluids, (posted 9/00), Lett. Math. Phys. 55: 193-204, 2001. 

R. Ghrist and R. Komendarczyk, Topological features of inviscid flows,  (updated 7/01),  in Geometry and Topology of Fluids, NATO ASI Series II vol. 47, Kluwer Press, 183-202, 2002.  

J. Etnyre and R. Ghrist, Contact topology and hydrodynamics III: knotted flowlines, (posted 6/99), Transactions of the Amer. Math. Soc., 352, 5781-5794, 2000. 

J. Etnyre and R. Ghrist, Contact topology and hydrodynamics II: solid tori, (posted 7/99, revised 1/01), Ergodic Theory & Dynamical Systems ,22 no. 3, 819--833, 2002.  

J. Etnyre and R. Ghrist, Contact topology and hydrodynamics I: Beltrami fields and the Seifert Conjecture, (revised, 2/99), Nonlinearity 13, 441-458, 2000. 

J. Etnyre and R. Ghrist, Contact topology and Anosov flows, (revised 9/99), in Topology & its Applications, 124  no. 2, 211--219, 2002.

J. Etnyre and R. Ghrist, Tight contact structures via dyanmics, (revised 7/98). Proc. Amer. Math. Soc., 127, 3697-3706, 1999. 

J. Etnyre and R. Ghrist, Stratified integrals and unknots in inviscid flows, (revised, 4/99), Contemporary Mathematics, 246, 99-112, 1999.

R. Ghrist, Braids and differential equations, (posted 12/00), Proceedings International Congress of Mathematicians, vol III, 2006, 1-26.

R. Ghrist and R.C. Vandervorst, Braids and scalar parabolic PDEs, (posted 4/04). Trans. Amer. Math. Soc., to appear.

R. Ghrist and E. Kin, Flowlines transverse to knot and link fibrations, (posted 1/03, revised 11/03). Pacific J. Math., 217(1), 61-86, 2004.

R. Ghrist, J.B.Vandenberg, and R.C. Vandervorst, Morse theory on spaces of braids with applications to Lagrangian dynamics, (posted 5/01, updated 10/02).  Invent. Math. 152(no.2), 369-432, 2003.

R. Ghrist and R. Vandervorst, Braids and parabolic dynamics,  (posted 6/02),  in Proceedings of New Directions in Dynamics Systems: Kyoto 2002.

R. Ghrist, J.B.Vandenberg, and R.C. Vandervorst, Closed characteristics of fourth-order twist systems via braids, (posted 4/00), Comptes Rendues de lAcademie des Sciences I, 331, 861-865, 2000. 

R. Ghrist, Resonant gluing bifurcations, (posted 9/99), Intl. J. Bifurcation and Chaos, 10 (9), 2141-2160, 2000. 

J. Etnyre and R. Ghrist, Gradient flows on plane fields, (revised 4/99), Commentarii Mathematici Helvetici, 74, 507-529, 1999.

R. Ghrist and T. Young, From Morse-Smale to all knots and links, Nonlinearity (11), 1111-1125, 1998.

R. Ghrist, Accumulations of infinite links, Topology and its Applications, (81), 171-184, 1997.

R. Ghrist, P. Holmes, and M. Sullivan, Knots and Links in Three-Dimensional Flows. Springer Lecture Notes in Mathematics, Volume 1654, Springer-Verlag, Berlin, 1997.

R. Ghrist, Branched 2-manifolds supporting all links, Topology, 36(2), 423-438, 1997.

R. Ghrist and P. Holmes, An ODE whose solutions contain all knots, Int. J. of Bifurcation and Chaos, 6(5), 779-800, 1996.

R. Ghrist, Flows on S3 supporting all links as orbits, Electronic Research Announcements of the AMS, 1(2), 91-97, 1995.

R. Ghrist and P. Holmes,
Knotting within the gluing bifurcation, in IUTAM Symposium on Nonlinearilty and Chaos in the Enginnering Dynamics, J. Thompson and S. Bishop, eds., John Wiley Press, 299-315, 1994.

R. Ghrist, Three examples of applied and computational homology, (posted 6/08), to appear in Nieuw Archief voor Wiskunde 5/9 no. 2, June 2008.

R. Ghrist, Barcodes: the persistent topology of data, (posted 11/06),  Amer. Math. Soc. Current Events Bulletin, Jan. 2007. Revised version in Bull. Amer. Math. Soc., 45(1), 61-75, 2008.

R. Ghrist, Configuration space, braids, and robotics, (posted 4/07), survey for summer school on braids & applications at the National University of Singapore.

V. de Silva and R. Ghrist, Homological sensor networks, (posted 11/05), Notices Amer. Math. Soc., 54(1), 2007, 10--17.

R. Ghrist, On the contact topology and geometry of ideal fluids, (posted 12/05), Handbook of Mathematical Fluid Dynamics vol. IV, 1-38, 2007.

R. Ghrist, Braids and differential equations, (posted 12/00),  Proceedings International Congress of Mathematicians, vol. III, 1-26, 2006.

R. Ghrist and R. Komendarczyk, Topological features of inviscid flows,  (updated 7/01),   Geometry and Topology of Fluids, NATO ASI Series II vol. 47, Kluwer Press, 183-202, 2002.

A. Abrams and R. Ghrist,  Finding topology in a factory: configuration spaces,  (posted 9/00), American Mathematics Monthly, 109, 140-150, February 2002. 

R. Ghrist, Chaotic knots and wild dynamics, Chaos, Solitons, and Fractals (9:4/5), 583-598, 1998.

Text Box: sensor networks
Text Box: geometric / topological robotics...
Text Box: contact topology and fluids...
Text Box: knots, links, and braids in dynamics...
Text Box: expository papers...
Text Box: paper topics