CURRICULUM VITAE

Richard S. Palais

Date of Birth: May 22, 1931

Education

Career

Principal Professional Positions:

Other Professional Positions and Honors:

 Note: All the books and papers listed below are available online for download as PDF files at Richard S. Palais' Books and Papers.

Published Monographs
  1. 1957 A Global Formulation of the Lie Theory of Transformation Groups, Memoirs of the AMS #22.
  2. 1960 The Classification of G-spaces, Memoirs of the AMS #36.
  3. 1964 Seminar on the Atiyah-Singer Index Theorem, Annals of Math. Study No. 4.
  4. 1968 Foundations of Global Non-linear Analysis, Benjamin & Co. NY.
  5. 1981 The Geometrization of Physics, Tsing-Hua University Press, Hsinchu, Taiwan.
  6. 1981 Real Algebraic Differential Topology, Mathematics Lecture Series #10, Publish or Perish Press Inc.
  7. 1988 Critical Point Theory and Submanifold Geometry, Lecture Notes in Mathematics #1353,Springer-Verlag, NY (with C.-L.Terng)
  8. 2009 (with Bob Palais) An Introduction to Ordinary Differential Equations and Classical Mechanics, AMS STML-51, ISBN-10: 0-8218-2138-5

Software Developed

  • 1995 -- 2010 3D-XplorMath --- A Mathematical Visualization Program for Macintosh Computers (http://3D-XplorMath.org)
  • 2005 -- 2010 The Virtual Mathematical Museum -- An interactive Mathematical Visualization website at http://VirtualMathMuseum.org

Research Publications (Note: All of the following are available online for download as PDF files at: Richard S. Palais' Books and Papers)

  1. A definition of the exterior derivative in terms of Lie derivatives, Proc. Amer. Math. Soc. 5 (1954) 902-908.
  2. A Global Formulation of the Lie Theory of Transformation Groups, Memoirs of the Amer. Math. Soc. 22 (1957).
  3. On the differentiability of isometries, Proc. Amer. Math. Soc. 8 (1957) 805-808.
  4. On a class of transformation groups, (with A.M. Gleason), Amer. J. Math. 79 (1957),631-648.
  5. Imbedding of compact, differentiable,transformation groups in orthogonal representations, J. Math. and Mech. 6 (1957), 674-678.
  6. A covering homotopy theory and the classification of G-spaces, Proc. Nat. Acad. Sci.U.S.A. 45 (1959), 857-859.
  7. Natural operations on differential forms, Trans. Amer. Math. Soc. 92 (1959),125-141.
  8. Extending diffeomorphisms, Proc. Amer. Math. Soc. 11 (1960), 274-277.
  9. The Classification of G-spaces, Memoirs of the Amer. Math. Soc. 36 (1960).
  10. Sprays, (with W. Ambrose and I. M. Singer), An. Acad. Brasil Ci. 32 (1960) 163-178.
  11. Slices and equivariant embeddings, (a chapter from Seminar on Transformation Groups, Ann. of Math. Study #6) 1960
  12. On the cohomology of Lie rings, Proc. of Symposim on Differential Geometry, Tucson, Feb. 1960.
  13. On the local triviality of the restriction map for embeddings, Comm. Math. Helv. 34 (1960), 306-312.
  14. Logarithmically exact differential forms, Proc. Amer. Math. Soc. 12 (1961), 50-52.
  15. Torus bundles over tori, (with T. E. Stewart), Proc. Amer. Math. Soc. 12 (1961), 26-40.
  16. On the existence of slices for actions of non-compact Lie groups, Annals of Math. 73 (1961), 295-323.
  17. The cohomology of differentiable transformation groups, (with T. E. Stewart) Amer. J. Math. 83 (1961), 623-644.
  18. Equivalence of nearly differentiable actions of a compact group, Bull. Amer. Math. Soc. 67 (1961), 362-364.
  19. Deformations of compact differentiable transformation groups, (with T. E. Stewart) Amer. J. Math. 82 (1960) 935-937.
  20. Uncountably many inequivalent actions of a compact group on R^n,(with R. Richardson), Proc. Amer. Math. Soc. 14 (1963), 374-377.
  21. Morse theory on Hilbert manifolds, Topology 2 (1963), 299-340.
  22. A generalized Morse theory, (with S. Smale), Research Announcement, Bull. Amer. Math. Soc. 70 (1964), 165-172.
  23. On the homotopy type of certain groups of operators, Topology 3 (1965) 271-279.
  24. Homeomorphic conjugacy of automorphisms on the Torus, (with L. Adler), Proc. Amer. Math. Soc. 16 (1965) 1222-1225.
  25. Seminar on the Atiyah-Singer Index Theorem, Annals of Math. Study, no.4, 1964, Princeton Univ. Press.
  26. Homotopy theory of infinite dimensional manifolds, Topology 5 (1966) 1-16.
  27. Lusternik-Schnirelman theory on Banach manifolds, Topology 5 (1966) 115-132.
  28. Foundations of Global Non-linear Analysis, Benjamin and Co. New York, 1968.
  29. The classification of real division algebras, Amer. Math. Monthly, 75, (1968 ) 366-368
  30. Manifolds of sections of fiber bundles and the calculus of variation, Proc.Symp.on Non-linear Analysis, vol. XVIII, Amer. Math. Soc. 195-205.
  31. Critical point theory and the minimax principle, Proc. Symp. on Global Analysis, vol. XV, Amer. Math. Soc. 185-212.
  32. The Morse Lemma for Banach spaces, Bull. Amer. Math. Soc. 75 (1969) 968-971.
  33. When proper maps are closed, Proc. Amer. Math. Soc. 24 (1969) 835
  34. C^1 action of compact Lie groups on compact manifolds are C^1 equivalent to C-infinity actions, Amer. Jour. Math. 88 (1970) 748-760.
  35. Banach manifolds of fiber bundle sections, Proc. International Cong. Math. Nice, 1970, vol. 2, 243-249, 1971.
  36. Natural bundles have finite order, (with C. L. Terng), Topology, 16 (1977) 271-277.
  37. A topological Gauss-Bonnet theorem, Jour. of Diff. Geometry, 13 (1978) 385-398.
  38. An analogue of Hartogs' theorem in an algebraic setting, Amer. Jour. Math. 100 (1978), 387-406.
  39. The Principal of Symmetric Criticality, Comm. Math. Physics, 69 (1979) 19-30.
  40. The Geometrization of Physics, Tsing Hua Univ., Hsinchu, Taiwan, 1981.
  41. Real Algebraic Differential Geometry, Math. Lecture series #10, Publish or Perish Inc. 1981.
  42. Warped product Einstein manifolds and Hessian PDE, (with A. Derdzinski and C.-L. Terng), preliminary report in Proc. of 1982 Munster Conference on Differential Geometry.
  43. Applications of the symmetric criticality principal in mathematical physics and differential geometry, Proc. Symp., Shanghai/China 1981, 247-301 (1984).
  44. Geometry and topology of isoparametric submanifolds, (with W. Y. Hsiang and C. L. Terng), (Research announcement), Proc. Nat. Acad. Sci. USA, 82(1985) 4863-4865.
  45. Reduction of variables for minimal submanifolds, (with C.L. Terng), Proc. Amer. Math. Soc., 98 (1986) 480-484.
  46. A general canonical form theorem, (with C.L. Terng), Transactions Amer. Math. Soc., 300 (1987) 771-789.
  47. Geometry of canonical forms, (with C.L. Terng), (Proceedings of the Kovaleskaya Symposium) Contemporary Mathematics, 64 (1987) 133-151.
  48. Topology of isoparametric submanifolds (with W.Y. Hsiang and C.L. Terng), Jour. of Diff. Geometry, 27 (1988) 423-460.
  49. Critical Point Theory and Submanifold Geometry, (with C.-L.Terng), Lecture Notes in Mathematics,#1353,(280 pages),Springer-Verlag, NY. 1988
  50. The Life and Mathematics of Shiing-Shen Chern, in "Chern---A Great Geometer of the Twentieth Century", edited by S.T. Yau, International Press, Hong Kong, 1992.
  51. Hyperpolar actions and k-flat homogeneous spaces, (with E. Heintze, G. Thorbergsson, and C.-L. Terng) J. reine angew. Math, 454 (1994) 163--179
  52. Symmetry, Criticality, and Condition C, In "Proceedings of the Sophus Lie Memorial Conference", edited by O. A. Laudal and B. Jahren, Scandinavian University Press (1994) 77-98
  53. Hyperpolar actions on symmetric spaces, (with E. Heintze, G. Thorbergsson, and C.-L. Terng) In "Geometry, Topology, and Physics For Raoul Bott", edited by S.T. Yau, International Press (1995) 214-245
  54. The Symmetries of Solitons, Bulletin. Amer. Math. Soc.,New Series 34, No. 4, 339-403 (1997) [ISSN 0273-0979] .
  55. The Visualization of Mathematics: Towards a Mathematical Exploratorium, Notices Amer. Math. Soc., 46, No.6 (June-July 1999)
  56. A Simple Proof of the Banach Contraction Principle, The Journal for Fixed Point Theory and its Applications, 2 (2007) 221--223
  57. Euler's Fixed Point Theorem: The Axis of a Rotation (with Bob Palais), The Journal for Fixed Point Theory and its Applications, 2 (2007) 215--220
  58. Linear and Nonlinear Waves and Solitons, in The Princeton Companion to Mathematics, T. Gower Ed., Princeton Univ. Press 2008, 234-239
  59. Euler's Theorem on the Axis of a Rotation: Proofs Old and New (with Bob Palais and Stephen Rodi), Amer. Math. Monthly, 116, (2009 ) 892-909

 

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Updated: March 9, 2010