Richard S. Palais

Date of Birth: May 22, 1931

Education

- 1952 B.A. Harvard College
- 1954 M.A. Harvard University
- 1956 Ph.D. Harvard University

Career

Principal Professional Positions:

- 1956-58 Instructor University of Chicago
- 1958-60 NSF Postdoctoral Fellow & Member, Princeton Institute for Advanced Study
- 1960-62 Assistant Professor, Brandeis University
- 1962-65 Associate Professor, Brandeis University
- 1965-2003 Professor, Brandeis University
- 2004- Adjunct Professor University of California at Irvine

Other Professional Positions and Honors:

- 1963-64 NSF Senior Postdoctoral Fellow & Member, Princeton Institute for Advanced Study
- 1965-67 Sloan Foundation Research Fellow
- 1966-68 Chairman, Dept. of Mathematics, Brandeis University
- 1968-69 Member, Princeton Institute for Advanced Study
- 1965-82 Editor, The Journal of Differential Geometry
- 1966-69 Editor, Transactions of the American Mathematical Society
- 1968-72 Member, NSF Advisory Panel for Mathematics
- 1970 Invited Speaker, International Congress of Mathematicians, Nice
- 1971-81 Trustee, American Mathematical Society
- 1974 Convenor of the Panel on Global Analysis and Analysis on Manifolds, Helsinki International Congress of Mathematicians
- 1974-75 Member, Princeton Institute for Advanced Study
- 1976-78 Professor, Univ. of Calif., SantaCruz (on leave from Brandeis)
- 1978-80 AMS Representative to CBMS
- 1979-83 Member, U.S. Committee for Mathematics
- 1979 Founding Chairman of TUG (TEX Users Group)
- 1980 Elected Fellow of AAAS
- 1981 Invited Speaker, US-China Symposium on Differential Geometry and Differential Equations, Shanghai-Anhui
- 1981-82 Gastprofessor, Universitat Bonn Member, Max-Planck-Institut fur Mathematik
- 1984-85 Member, Mathematical Sciences Research Institute, Berkeley
- 1987 Visiting Professor, Nankai Institute of Mathematics, Tianjin, China
- 1987 Chairman, AMS Committee on Communications
- 1988-89 Chairman, AMS Committee on the Electronic Exchange of Information
- 1990-1995 Managing Editor, Bulletin of the AMS, Research Expository Papers
- 1993-1995 Chair of the AMS Committee on Publication Policy
- 1996-1997 Chair of the AAAS Section A (Mathematics)
- 2006 Awarded First Prize for Illustration, with partner Luc Bénard, in NSF/Science Magazine 2006 International Science and Engineering Visualization Challenge
- 2007- Editor for Surveys and Research Expository
Papers, The Journal for Fixed Point Theory and its

Applications - 2009 Awarded First Prize for Illustration, with partner Luc Bénard, in NSF/Science Magazine 2006 International Science and Engineering Visualization Challenge

Published Monographs

- 1957 A Global Formulation of the Lie Theory of Transformation Groups, Memoirs of the AMS #22.
- 1960 The Classification of G-spaces, Memoirs of the AMS #36.
- 1964 Seminar on the Atiyah-Singer Index Theorem, Annals of Math. Study No. 4.
- 1968 Foundations of Global Non-linear Analysis, Benjamin & Co. NY.
- 1981 The Geometrization of Physics, Tsing-Hua University Press, Hsinchu, Taiwan.
- 1981 Real Algebraic Differential Topology, Mathematics Lecture Series #10, Publish or Perish Press Inc.
- 1988 Critical Point Theory and Submanifold Geometry, Lecture Notes in Mathematics #1353,Springer-Verlag, NY (with C.-L.Terng)
- 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)

- A definition of the exterior derivative in terms of Lie derivatives, Proc. Amer. Math. Soc. 5 (1954) 902-908.
- On the differentiability of isometries, Proc. Amer. Math. Soc. 8 (1957) 805-808.
- A Global Formulation of the Lie Theory of Transformation Groups, Memoirs of the Amer. Math. Soc. 22 (1957).
- On a class of transformation groups, (with A.M. Gleason), Amer. J. Math. 79 (1957),631-648.
- Imbedding of compact, differentiable,transformation groups in orthogonal representations, J. Math. and Mech. 6 (1957), 674-678.
- A covering homotopy theory and the classification of G-spaces, Proc. Nat. Acad. Sci.U.S.A. 45 (1959), 857-859.
- Natural operations on differential forms, Trans. Amer. Math. Soc. 92 (1959),125-141.
- Extending diffeomorphisms, Proc. Amer. Math. Soc. 11 (1960), 274-277.
- Slices and equivariant embeddings, (a chapter from Seminar on Transformation Groups, Ann. of Math. Study #6) 1960
- Sprays, (with W. Ambrose and I. M. Singer), An. Acad. Brasil Ci. 32 (1960) 163-178.
- The Classification of G-spaces, Memoirs of the Amer. Math. Soc. 36 (1960).
- On the cohomology of Lie rings, Proc. of Symposim on Differential Geometry, Tucson, Feb. 1960.
- On the local triviality of the restriction map for embeddings, Comm. Math. Helv. 34 (1960), 306-312.
- Logarithmically exact differential forms, Proc. Amer. Math. Soc. 12 (1961), 50-52.
- Torus bundles over tori, (with T. E. Stewart), Proc. Amer. Math. Soc. 12 (1961), 26-40.
- On the existence of slices for actions of non-compact Lie groups, Annals of Math. 73 (1961), 295-323.
- The cohomology of differentiable transformation groups, (with T. E. Stewart) Amer. J. Math. 83 (1961), 623-644.
- Equivalence of nearly differentiable actions of a compact group, Bull. Amer. Math. Soc. 67 (1961), 362-364.
- Deformations of compact differentiable transformation groups, (with T. E. Stewart) Amer. J. Math. 82 (1960) 935-937
- Morse theory on Hilbert manifolds, Topology 2 (1963), 299-340.
- Uncountably many inequivalent actions of a compact group on R^n,(with R. Richardson), Proc. Amer. Math. Soc. 14 (1963), 374-377.
- A generalized Morse theory, (with S. Smale), Research Announcement, Bull. Amer. Math. Soc. 70 (1964), 165-172.
- Seminar on the Atiyah-Singer Index Theorem, Annals of Math. Study, no.4, 1964, Princeton Univ. Press.
- On the homotopy type of certain groups of operators, Topology 3 (1965) 271-279.
- Homeomorphic conjugacy of automorphisms on the Torus, (with L. Adler), Proc. Amer. Math. Soc. 16 (1965) 1222-1225.
- Homotopy theory of infinite dimensional manifolds, Topology 5 (1966) 1-16.
- Lusternik-Schnirelman theory on Banach manifolds, Topology 5 (1966) 115-132.
- Foundations of Global Non-linear Analysis, Benjamin and Co. New York, 1968.
- The classification of real division algebras, Amer. Math. Monthly, 75, (1968 ) 366-368
- Manifolds of sections of fiber bundles and the calculus of variation, Proc.Symp.on Non-linear Analysis, vol. XVIII, Amer. Math. Soc. 195-205.
- Critical point theory and the minimax principle, Proc. Symp. on Global Analysis, vol. XV, Amer. Math. Soc. 185-212.
- The Morse Lemma for Banach spaces, Bull. Amer. Math. Soc. 75 (1969) 968-971.
- When proper maps are closed, Proc. Amer. Math. Soc. 24 (1969) 835
- 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.
- Banach manifolds of fiber bundle sections, Proc. International Cong. Math. Nice, 1970, vol. 2, 243-249, 1971.
- Natural bundles have finite order, (with C. L. Terng), Topology, 16 (1977) 271-277.
- A topological Gauss-Bonnet theorem, Jour. of Diff. Geometry, 13 (1978) 385-398.
- An analogue of Hartogs' theorem in an algebraic setting, Amer. Jour. Math. 100 (1978), 387-406.
- The Principal of Symmetric Criticality, Comm. Math. Physics, 69 (1979) 19-30.
- The Geometrization of Physics, Tsing Hua Univ., Hsinchu, Taiwan, 1981.
- Real Algebraic Differential Geometry, Math. Lecture series #10, Publish or Perish Inc. 1981.
- 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.
- Applications of the symmetric criticality principal in mathematical physics and differential geometry, Proc. Symp., Shanghai/China 1981, 247-301 (1984).
- 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.
- Reduction of variables for minimal submanifolds, (with C.L. Terng), Proc. Amer. Math. Soc., 98 (1986) 480-484.
- A general canonical form theorem, (with C.L. Terng), Transactions Amer. Math. Soc., 300 (1987) 771-789.
- Geometry of canonical forms, (with C.L. Terng), (Proceedings of the Kovaleskaya Symposium) Contemporary Mathematics, 64 (1987) 133-151.
- Topology of isoparametric submanifolds (with W.Y. Hsiang and C.L. Terng), Jour. of Diff. Geometry, 27 (1988) 423-460.
- Critical Point Theory and Submanifold Geometry, (with C.-L.Terng), Lecture Notes in Mathematics,#1353,(280 pages),Springer-Verlag, NY. 1988
- 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.
- Hyperpolar actions and k-flat homogeneous spaces, (with E. Heintze, G. Thorbergsson, and C.-L. Terng) J. reine angew. Math, 454 (1994) 163--179
- 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
- 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
- The Symmetries of Solitons, Bulletin. Amer. Math. Soc.,New Series 34, No. 4, 339-403 (1997) [ISSN 0273-0979] .
- The Visualization of Mathematics: Towards a Mathematical Exploratorium, Notices Amer. Math. Soc., 46, No.6 (June-July 1999)
- A Simple Proof of the Banach Contraction Principle, The Journal for Fixed Point Theory and its Applications, 2 (2007) 221--223
- 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
- Linear and Nonlinear Waves and Solitons, in The Princeton Companion to Mathematics, T. Gower Ed., Princeton Univ. Press 2008, 234-239
- An Introduction to Ordinary Differential Equations and Classical Mechanics, (with Robert A. Palais) AMS STML-51, ISBN-10: 0-8218-2138-5 2009)
- 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

- The Initial Value Problem for Weakly Nonlinear PDE

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Updated: March 9, 2010