Peter Olver's Additional Publications

Last updated:   May 21, 2019


Recent (and not so recent) Preprints

  1. O'Neill, R., Angulo-Umana, P., Calder, J., Hessburg, B., Olver, P.J., Shakiban, C., and Yezzi-Woodley, K., Computation of circular area and spherical volume invariants via boundary integrals, preprint, 2019.   pdf
  2. Olver, P.J., Invariants of finite and discrete group actions via moving frames, preprint, 2019.   pdf
  3. Olver, P.J., Sheils, N.E., and Smith, D.A., Revivals and fractalisation in the linear free space Schrödinger equation, preprint, 2018.   pdf      movies
  4. Olver, P.J., Dispersive fractalization in Fermi-Pasta-Ulam lattices I. The linear regime, preprint, 2018.   pdf
  5. Kang, J., Liu, X., Olver, P.J., and Qu, C., Liouville correspondences between multi-component integrable hierarchies, preprint, 2018.   pdf
  6. Tuznik, S.L., Olver, P.J., and Tannenbaum, A., Equi-affine differential invariants for invariant feature point detection, European J. Appl. Math., to appear.   pdf
  7. Gün Polat, G., and Olver, P.J., Joint differential invariants of binary and ternary forms, preprint, 2017.   pdf
  8. Olver, P.J., Equivariant moving frames for Euclidean surfaces, preprint, 2016.   pdf
  9. Olver, P.J., Moving frame derivation of the fundamental equi-affine differential invariants for level set functions, preprint, 2015.   pdf
  10. Calabi, E., Olver, P.J., and Tannenbaum, A., Invariant numerical approximations to differential invariant signatures, preprint, University of Minnesota, 1995.   pdf
  11. González-López, A., Kamran, N., and Olver, P.J., Quasi-exact solvability in the real domain, preprint, University of Minnesota, 1995.   pdf
  12. Olver, P.J., Invariant theory of biforms, preprint, University of Minnesota, 1986.   Scanned:  pdf
  13. Olver, P.J., Differential hyperforms I, preprint, University of Minnesota, 1982.   Scanned:  pdf
  14. Olver, P.J., On the construction of deformations of integrable systems, preprint, University of Minnesota, 1981.   Scanned:  pdf
  15. Olver, P.J., Symmetry groups and conservation laws in the formal variational calculus, preprint, University of Oxford, 1978.   Scanned:  pdf
  16. Olver, P.J., On the symmetry group of a linear partial differential equation, preprint, University of Chicago, 1977.   Scanned:  pdf
  17. Olver, P.J., Symmetry groups of partial differential equations, thesis, Harvard University, 1976.   Scanned:  pdf
  18. Olver, P.J., Some applications of spline functions to problems in computer graphics, senior honors thesis, Brown University, 1973.   Scanned:  pdf

Appendices and Chapters in Books

  1. Olver, P.J., Lie algebras and Lie groups, in: Encyclopedia of Nonlinear Science, A. Scott, ed., Routledge, New York, 2004.   pdf
  2. Olver, P.J., Lie groups and differential equations, in: The Concise Handbook of Algebra, A.V. Mikhalev and G.F. Pilz, eds., Kluwer Acad. Publ., Dordrecht, Netherlands, 2002, pp. 92-97.   pdf
  3. Olver, P.J., and Vorob'ev, E.M., Nonclassical and conditional symmetries, in: CRC Handbook of Lie Group Analysis of Differential Equations, vol. 3, N.H. Ibragimov, ed., CRC Press, Boca Raton, Fl., 1996, pp. 291-328.   pdf
  4. Olver, P.J., Sapiro, G., and Tannenbaum, A., Differential invariant signatures and flows in computer vision: a symmetry group approach, in: Geometry-Driven Diffusion in Computer Vision, B. M. Ter Haar Romeny, ed., Kluwer Acad. Publ., Dordrecht, Netherlands, 1994, pp. 255-306.   pdf
  5. González-López, A., Kamran, N., and Olver, P.J., Quasi-exact solvability in higher dimensions, appendix in: Quasi-Exact Solvability, A.G. Ushveridze, Adam Hilger, Bristol, 1994.   
  6. Olver, P.J., How to find the symmetry group of a differential equation, appendix in: Group Theoretic Methods in Bifurcation Theory, D.H. Sattinger, Lecture Notes in Mathematics, vol. 762, Springer-Verlag, New York, 1979.   

Contributions to Conference Proceedings

  1. Olver, P.J., Normal forms for submanifolds under group actions, in: Symmetries, Differential Equations and Applications, V. Kac, P.J. Olver, P. Winternitz, and T. Özer, eds., Proceedings in Mathematics & Statistics, Springer, New York, 2018, pp. 3-27.   pdf
  2. Olver, P.J., Lectures on moving frames, in: Symmetries and Integrability of Difference Equations, D. Levi, P. Olver, Z. Thomova, and P. Winternitz, eds., London Math. Soc. Lecture Note Series, vol. 381, Cambridge University Press, Cambridge, 2011, pp. 207-246.   pdf
  3. Olver, P.J., Recent advances in the theory and application of Lie pseudo-groups, in: XVIII International Fall Workshop on Geometry and Physics, M. Asorey, J.F. Cariñena, J. Clemente-Gallardo, and E. Martínez, AIP Conference Proceedings, vol. 1260, American Institute of Physics, Melville, NY, 2010, pp. 35-63.   pdf
  4. Olver, P.J., Invariant variational problems and invariant flows via moving frames, in: Variations, Geometry and Physics, O. Krupková and D. Saunders, eds., Nova Science Publ., New York, 2009, pp. 209-235.   pdf
  5. Olver, P.J., and Pohjanpelto, J., Pseudo-groups, moving frames, and differential invariants, in: Symmetries and Overdetermined Systems of Partial Differential Equations, M. Eastwood and W. Miller, Jr., eds., IMA Volumes in Mathematics and Its Applications, vol. 144, Springer-Verlag, New York, 2008, pp. 127-149.   pdf
  6. Olver, P.J., and Pohjanpelto, J., Differential invariants for Lie pseudo-groups, in: Gröbner Bases in Symbolic Analysis; M. Rosenkranz, D. Wang, eds, Radon Series Comp. Appl. Math., vol. 2, Walter de Gruyter, Berlin, 2007, pp. 217-243.   pdf
  7. Olver, P.J., and Pohjanpelto, J., Moving frames and differential invariants for Lie pseudo-groups, in: Symmetry and Perturbation Theory, G. Gaeta, R. Vitolo, and S. Walcher, eds., World Scientific, Singapore, 2007, pp. 172-180.   pdf
  8. Welk, M., Kim, P., and Olver, P.J., Numerical invariantization for morphological PDE schemes, in: Scale Space and Variational Methods in Computer Vision, F. Sgallari, A. Murli, and N. Paragios, eds., Lecture Notes in Computer Science, vol. 4485, Springer-Verlag, New York, 2007, pp. 508-519.   pdf
  9. Rathi, Y., Olver, P.J., Sapiro, G., and Tannenbaum, A., Affine invariant surface evolutions for 3D image segmentation, in: Image Processing: Algorithms and Systems, Neural Networks, and Machine Learning, E.R. Dougherty, J.T. Astola, K.O. Egiazarian, N.M. Nasrabadi, and S.A. Rizvi, eds., vol. 6064, SPIE Press, Bellingham, Wash., 2006, pp. 606401.   pdf
  10. Olver, P.J., A survey of moving frames, in: Computer Algebra and Geometric Algebra with Applications, H. Li, P.J. Olver, and G. Sommer, eds., Lecture Notes in Computer Science, vol. 3519, Springer-Verlag, New York, 2005, pp. 105-138.   pdf
  11. Olver, P.J., and Pohjanpelto, J., Regularity of pseudogroup orbits, in: Symmetry and Perturbation Theory, G. Gaeta, B. Prinari, S. Rauch-Wojciechowski, and S. Terracini, eds., World Scientific, Singapore, 2005, pp. 244-254.   pdf
  12. Olver, P.J., An introduction to moving frames, in: Geometry, Integrability and Quantization; vol. 5, I.M. Mladenov and A.C. Hirschfeld, eds., Softex, Sofia, Bulgaria, 2004, pp. 67-80.   pdf
  13. Olver, P.J., Nonlocal symmetries and ghosts, in: New Trends in Integrability and Partial Solvability, A.B. Shabat et. al., eds., Kluwer Acad. Publ., Dordrecht, Netherlands, 2004, pp. 199-215.   pdf
  14. Georgiou, T., Olver, P.J., and Tannenbaum, A., Maximal entropy for reconstruction of back projection images, in: Mathematical Methods in Computer Vision, P.J. Olver and A. Tannenbaum, eds., IMA Volumes in Mathematics and its Applications, vol. 133, Springer-Verlag, New York, 2003, pp. 57-64.   pdf
  15. Olver, P.J., Moving frames: a brief survey, in: Symmetry and Perturbation Theory, D. Bambusi, M. Cadoni, and G. Gaeta, eds., World Scientific, Singapore, 2001, pp. 143-150.   pdf
  16. Olver, P.J., Sanders, J., and Wang, J.P., Classification of symmetry-integrable evolution equations, in: Bäcklund and Darboux Transformations. The Geometry of Solitons, A. Coley, D. Levi, R. Milson, C. Rogers, and P. Winternitz, eds., CRM Proceedings & Lecture Notes, vol. 29, 2001, pp. 363-372.   pdf
  17. Olver, P.J., Moving frames — in geometry, algebra, computer vision, and numerical analysis, in: Foundations of Computational Mathematics, R. DeVore, A. Iserles, and E. Suli, eds., London Math. Soc. Lecture Note Series, vol. 284, Cambridge University Press, Cambridge, 2001, pp. 267-297.   pdf
  18. Fels, M., and Olver, P.J., Moving frames and moving coframes, in: Algebraic Methods in Physics, Y. Saint-Aubin and L. Vinet, eds., CRM Series in Math. Phys., Springer-Verlag, New York, 2001, pp. 47-64.   pdf
  19. Foursov, M.V., and Olver, P.J., On the classification of symmetrically-coupled integrable evolution equations, in: Symmetries and Differential Equations, V.K. Andreev and Yu.V. Shanko, eds, Institute of Computational Modelling, Krasnoyarsk, Russia, 2000, pp. 244-248.   pdf
  20. Olver, P.J., Moving frames, RIMS Kokyuroku 1150 (2000), 114-124.   pdf
  21. Li, Y.A., Olver, P.J., and Rosenau, P., Non-analytic solutions of nonlinear wave equations, in: Nonlinear Theory of Generalized Functions, M. Grosser, G. Hormann, M. Kunzinger, and M. Oberguggenberger, eds., Research Notes in Mathematics, vol. 401, Chapman and Hall/CRC, New York, 1999, pp. 129-145.   pdf
  22. Olver, P.J., A quasi-exactly solvable travel guide, in: GROUP21: Physical Applications and Mathematical Aspects of Geometry, Groups, and Algebras, vol. 1, H.-D. Doebner, W. Scherer, and P. Nattermann, eds., World Scientific, Singapore, 1997, pp. 285-295.   pdf
  23. Heredero, R.H., Olver, P.J., Classification of invariant wave equations, in: GROUP21: Physical Applications and Mathematical Aspects of Geometry, Groups, and Algebras, vol. 2, H.-D. Doebner, W. Scherer, and C. Schulte, eds., World Scientific, Singapore, 1997, pp. 1010-1016.   pdf
  24. Fokas, A.S., Olver, P.J., and Rosenau, P., A plethora of integrable bi-Hamiltonian equations, in: Algebraic Aspects of Integrable Systems: In Memory of Irene Dorfman, A.S. Fokas and I.M. Gel'fand, eds., Progress in Nonlinear Differential Equations, vol. 26, Birkhäuser, Boston, 1996, pp. 93-101.   pdf
  25. Olver, P.J., Sapiro, G., and Tannenbaum, A., Affine invariant gradient flows, in: ICAOS '96: Images, Wavelets and PDE's, M.-O. Berger, et. al., eds., Lecture Notes in Control and Information Sciences, vol. 219, Springer-Verlag, New York, 1996, pp. 194-200.   pdf
  26. Olver, P.J., Sapiro, G., and Tannenbaum, A., Affine invariant detection: edges, active contours, and segments, in: Proceedings 1996 IEEE Computer Society Conference on Computer Vision and Pattern Recognition Proceedings, IEEE Computer Soc. Press, Los Alamitos, CA, 1996, pp. 520-525.   pdf
  27. Yezzi, A., Kichenassamy, S., Kumar, A., Olver, P., and Tannenbaum, A., A gradient surface evolution approach to 3D segmentation, in: Proceedings of the IS&T's 49th Annual Conference; Society for Imaging Science and Technology, Springfield, Virginia, 1996, pp. 305-307   pdf
  28. Finkel, F., González-López, A., Kamran, N., Olver, P.J., and Rodriguez, M.A., Lie algebras of differential operators and partial integrability, in: Proceedings of IV Workshop on Differential Geometry and its Applications; Santiago de Compostela, Spain, 1995.   pdf
  29. Kumar, A., Yezzi, A., Kichenassamy, S., Olver, P.J., Tannenbaum, A., Active contours for visual tracking: a geometric gradient based approach, in: Proceedings of the 34th Conference on Decision and Control, IEEE Computer Soc. Press, Piscataway, N.J., 1995, pp. 4041-4046.   pdf
  30. Kichenassamy, S., Kumar, A., Olver, P.J., Tannenbaum, A., and Yezzi, A., Gradient flows and geometric active contour models, in: Fifth International Conference on Computer Vision, IEEE Computer Soc. Press, Cambridge, Mass., 1995, pp. 810-815.   pdf
  31. Olver, P.J., Higher order models for water waves, in: Geometrical Methods in Fluid Dynamics, R. Salmon and B. Ewing-Deremer, eds., Woods Hole Oceanographic Institution, Technical Report WHOI-94-12, Woods Hole, MA, 1994, pp. 327-331.   Scanned:  pdf
  32. Anderson, I.M., Kamran, N., and Olver, P.J., Internal symmetries of differential equations, in: Modern Group Analysis: Advanced Analytical and Computational Methods in Mathematical Physics, N.H. Ibragimov, M. Torrisi, and A. Valenti, eds., Kluwer, Dordrecht, Netherlands, 1993, pp. 7-21.   pdf
  33. Olver, P.J., Canonical forms for biHamiltonian systems, in: The Verdier Memorial Conference on Integrable Systems, O. Babelon, P. Cartier, and Y. Kosmann-Schwarzbach eds., Progress in Math., Birkhäuser, Boston, 1993, pp. 239-249.   pdf
  34. González-López, A., Kamran, N., and Olver, P.J., New quasi-exactly solvable Hamiltonians in two dimensions, in: Group Theoretic Methods in Physics, M.A. del Olmo, M. Santander, and J. Mateos Guilarte, eds., Proc. XIX International Colloquium, Anales de Física Monografias, Editorial Ciemat, Madrid, 1992, Vol. I, pp. 233-236.   pdf
  35. Olver, P.J., Canonical forms for compatible biHamiltonian systems, in: Solitons and Chaos, I. Antoniou, and F. Lambert, eds., Springer-Verlag, New York, 1991, pp. 171-179.   Scanned:  pdf
  36. González-López, A., Kamran, N., and Olver, P.J., Lie algebras of first order differential operators in two complex variables, in: Differential Geometry, Global Analysis, and Topology, A. Nicas and W.F. Shadwick, eds., Canadian Math. Soc. Conference Proceedings, vol. 12, Amer. Math. Soc., Providence, R.I., 1991, pp. 51-84.   
  37. Olver, P.J., Canonical anisotropic elastic moduli, in: Modern Theory of Anisotropic Elasticity and Applications, J.J. Wu, T.C.T. Ting, and D.M. Barnett, eds., SIAM, Philadelphia, 1991, pp. 325-339.   Scanned:  pdf
  38. Olver, P.J., Internal symmetries of differential equations, in: Differential Equations and Computer Algebra, M. Singer, ed., Academic Press, New York, 1991, pp. 1-28.   
  39. Olver, P.J., Invariant theory, equivalence problems and the calculus of variations, in: Invariant Theory and Tableaux, D. Stanton, ed., IMA Volumes in Mathematics and Its Applications, vol. 19, Springer-Verlag, New York, 1990, pp. 59-81.   pdf
  40. Olver, P.J., Recursion operators and Hamiltonian systems, in: Symmetries and Nonlinear Phenomena, D. Levi and P. Winternitz, eds., CIF Series, Vol. 9, World Scientific, Singapore, 1988, pp. 222-249.   Scanned:  pdf
  41. Olver, P.J., Generalized symmetries, in: XV International Colloquium on Group Theoretical Methods in Physics, R. Gilmore, ed., World Scientific, Singapore, 1987, pp. 216-228.   
  42. Olver, P.J., Conservation laws in continuum mechanics, in: Non-classical Continuum Mechanics, R.J. Knops and A.A. Lacey, eds., London Math. Soc. Lecture Note Series #122, Cambridge Univ. Press, Cambridge, 1987, pp. 96-107.   Scanned:  pdf
  43. Olver, P.J., BiHamiltonian systems, in: Ordinary and Partial Differential Equations, B.D. Sleeman and R.J. Jarvis, eds., Pitman Research Notes in Mathematics Series, No. 157, Longman Scientific and Technical, New York, 1987, pp. 176-193.   Scanned:  pdf
  44. Olver, P.J., Invariant theory and differential equations, in: Invariant Theory, S.S. Koh, ed., Lecture Notes in Mathematics, vol. 1278, Springer-Verlag, New York, 1987, pp. 62-80.   Scanned:  pdf
  45. Olver, P.J., Noether's theorems and systems of Cauchy-Kovalevskaya type, in: Nonlinear Systems of Partial Differential Equations in Applied Mathematics, B. Nicholaenko, D.D. Holm, and J.M. Hyman, eds., Lectures in Applied Math., vol. 23, part 2, Amer. Math. Soc., Providence, R.I., 1986, pp. 81-104.   Scanned:  pdf
  46. Olver, P.J., Symmetry groups and path-independent integrals, in: Fundamentals of Deformation and Fracture, B.A. Bilby, K.J. Miller and J.R. Willis, eds., Cambridge Univ. Press, New York, 1985, pp. 57-71.   Scanned:  pdf
  47. Olver, P.J., Hamiltonian and non-Hamiltonian models for water waves, in: Trends and Applications of Pure Mathematics to Mechanics, P.G. Ciarlet and M. Roseau, eds., Lecture Notes in Physics No. 195, Springer-Verlag, New York, 1984, pp. 273-290.   Scanned:  pdf
  48. Olver, P.J., and Shakiban, C., A resolution of the Euler operator, in: Proceedings of the Eighth National Mathematics Conference, M. Nouri-Moghadam, ed., Arya-Mehr Univ. Tech., Tehran, Iran, 1977, pp. 325-337.   

Expository Papers

  1. Olver, P.J., The world digital mathematics library: report of a panel discussion, in: Proceedings of the International Congress of Mathematicians, Seoul, Korea, 2014, vol. 1, to appear.
  2. Olver, P.J., Journals in flux, Notices Amer. Math. Soc. 58 (2011), 1124-1126.   pdf
  3. Olver, P.J., From the Chair of the Committee on Electronic Information and Communication (CEIC), IMU-Net 45, January 2011.
  4. Lozier, D. and Olver, P., The Digital Library of Mathematical Functions, IMU-Net 33, January 2009.

Book Reviews

  1. Neuenschwander, D.E., Emmy Noether's Wonderful Theorem, revised ed., Johns Hopkins Univ. Press, Baltimore, MD, 2017 — in: American J. Physics 86 (2018), 955-957.
  2. Ibragimov, N.H., Transformation groups and Lie algebras, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2013 — in: MathSciNet (2015), MR3236114.
  3. Kosmann-Schwarzbach, Y., The Noether Theorems. Invariance and Conservation Laws in the Twentieth Century, translated by B.E. Schwarzbach, Springer, New York, 2011 — in: Bull. Amer. Math. Soc. 50 (2013), 161-167.
  4. Goodman, R., and Wallach, N.R., Symmetry, Representations, and Invariants, Graduate Texts in Mathematics, vol. 255, Springer, New York, 2009 — in: SIAM Review 53 (2011), 599-600.
  5. Mansfield, E.L., A Practical Guide to the Invariant Calculus, Cambridge University Press, Cambridge, 2010 — in: SIAM Review 53 (2011), 596-599.
  6. Gadea, P.M., and Munoz Masque, J., Analysis and Algebra on Differentiable Manifolds: A Workbook for Students and Teachers, Springer, New York, 2009 — in: SIAM Review 53 (2011), 202-203.
  7. Gilmore, R., Lie Groups, Physics, and Geometry. An Introduction for Physicists, Engineers, and Chemists, Cambridge University Press, New York, 2008 — in: Physics Today 62 (3) (2009), 55-56.
  8. Schwarz, F., Algorithmic Lie Theory for Solving Ordinary Differential Equations, Chapman & Hall/CRC, Boca Raton, Fl, 2008 — in: Math. Reviews, MR2351266 (2009a:34015).
  9. Bryant, R., Griffiths, P., and Grossman, D., Exterior Differential Systems and Euler-Lagrange Partial Differential Equations, University of Chicago Press, 2003 — in: Bull. Amer. Math. Soc. 42 (2005), 407-412.
  10. Lee, J.M., Introduction to Smooth Manifolds, Graduate Texts in Mathematics, vol. 218, Springer-Verlag, New York, 2003 — in: SIAM Review 46 (2004), 179-180.
  11. Hydon, P.E., Symmetry Methods for Differential Equations, Cambridge University Press, Cambridge, 2000 — in: Zeit. Angew. Math. Mechanik 81 (2001), 612.
  12. Andreev, V.K., Kaptsov, O.V., Pukhanachov, V.V., and Rodinov, A.A., Applications of Group-Theoretical Methods in Hydrodynamics, Kluwer Academic Publ., Dordrecht, Netherlands, 1998 — in: Zeit. Angew. Math. Physik 52 (2001), 896-897.
  13. Duistermaat, J.J., and Kolk, J.A.C., Lie Groups, Springer-Verlag, New York, 1999 — in: SIAM Review 43 (2001), 399-400.
  14. Krasil'shchik, I.S., and Vinogradov, A.M., eds., Symmetries of Differential Equations in Mathematical Physics, American Mathematical Society, 1998 — in: Bull. Amer. Math. Soc. 37 (2000), 369-371.
  15. Fushchich, W.I., and Nikitin, A.G., Symmetries of Equations of Quantum Mechanics, Allerton Press, New York, 1994 — in: Foundations of Physics 77 (1995), 297.
  16. Dorfman, I., Dirac Structures and Integrability of Nonlinear Evolution Equations, Nonlinear Science: Theory and Applications, J. Wiley & Sons, New York, 1993 — in: Bull. Amer. Math. Soc. 31 (1994), 305-308.
  17. Zharinov, V.V., Geometrical Aspects of Partial Differential Equations, World Scientific, Singapore, 1992 — in: SIAM Review 35 (1993), 675-676.
  18. Golubitsky, M., and Stewart, I., Fearful Symmetry: Is God a Geometer?, Blackwell, Oxford, 1992 — in: SIAM News 26 (1) (1993), 9, 19.
  19. Stephani, H., Differential Equations: Their Solution Using Symmetries, Cambridge University Press, Cambridge, 1989 — in: SIAM Review 33 (1991), 330-332.
  20. Rogers, C., and Ames, W.F., Nonlinear Boundary Value Problems in Science and Engineering, Academic Press, New York, 1989 — in: Math. of Computation, 55 (1990), 873-874.
  21. Bluman, G.W., and Kumei, S., Symmetries and Differential Equations, Springer-Verlag, New York, 1989 — in: SIAM Review 32 (1990), 517-519.
  22. Fushchich, W.I., and Nikitin, A.G., Symmetries of Maxwell's Equations, Mathematics and its Applications (Soviet Series), D. Reidel Publ. Co., Boston, 1987 — in: American Scientist 77 (1989), 297.
  23. Fushchich, W.I., and Nikitin, A.G., Symmetries of Maxwell's Equations, Mathematics and its Applications (Soviet Series), D. Reidel Publ. Co., Boston, 1987 — in: Bull. Amer. Math. Soc. 19 (1988), 545-550.
  24. Ibragimov, N.H., Transformation Groups Applied to Mathematical Physics, Mathematics and its Applications (Soviet Series), D. Reidel Publ. Co., Boston, 1985 — in: American Scientist 75 (1987), 211-212.