Richard S. PalaisAdjunct Professor, Mathematics 

Research Interests 
Mathematical Visualization  
URLs  My UCI Homepage  
Home Page for my Mathematical Visualization Program 3DXplorMath (including free download section)  
The Virtual Math Museum is an online mathematical museum that I have set up and maintain.  
Academic Distinctions 
196364 NSF Senior Postdoctoral Fellow & Member, Princeton Institute for Advanced Study 196567 Sloan Foundation Research Fellow 196582 Editor, The Journal of Differential Geometry 196668 Chairman, Dept. of Mathematics, Brandeis University 196869 Member, Princeton Institute for Advanced Study 196582 Editor, The Journal of Differential Geometry 196669 Editor, Transactions of the American Mathematical Society 196872 Member, NSF Advisory Panel for Mathematics 1970 Invited Speaker, International Congress of Mathematicians, Nice 197181 Trustee, American Mathematical Society 1974 Convenor of the Panel on Global Analysis and Analysis on Manifolds, Helsinki International Congress of Mathematicians 197475 Member, Princeton Institute for Advanced Study 197678 Professor, Univ. of Calif., SantaCruz (on leave from Brandeis) 197880 AMS Representative to CBMS 197983 Member, U.S. Committee for Mathematics 1979 Founding Chairman of TUG (TEX Users Group) 1980 Elected Fellow of AAAS 1981 Invited Speaker, USChina Symposium on Differential Geometry and Differential Equations, ShanghaiAnhui 198182 Gastprofessor, Universitat Bonn Member, MaxPlanckInstitut fur Mathematik 198485 Member, Mathematical Sciences Research Institute, Berkeley 1987 Visiting Professor, Nankai Institute of Mathematics, Tianjin, China 1987 Chairman, AMS Committee on Communications 198889 Chairman, AMS Committee on the Electronic Exchange of Information 19901995 Managing Editor, Bulletin of the AMS, Research Expository Papers 19961997 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 

Research Abstract 
In recent years I have become interested in mathematical visualization, and one of my major ongoing projects is the development and continued improvement of a program called 3DXplorMath. This is a tool for aiding in the visualization of a wide variety of mathematical objects and processes. Based on what I have learned from my experience in writing this program, I wrote an essay called "The Visualization of Mathematics: Towards a Mathematical Exploratorium" that appeared in the June/July 1999 issue of the Notices of the American Mathematical Society. With the help of Xah Lee, and Luc Benard I have created a Gallery of visualizations, mostly produced using 3DXplorMath. Luc Benard and I won first prize in the NSF/Science Magazine Scientific Visualization Challenge in 2006 and again in 2009. Our 2006 entry appeared on the cover of the Sept. 22,2006 issue of Scince Magazine. I have also recently been thinking about integrable, onedimensional wave equationsan area that is usually referred to as soliton mathematics. I wrote an expository article for the Bulletin of the AMS (October 1997 issue) called The Symmetries of Solitons and I was invited to write an article on wave equations for the Princeton Companion to Mathematics 

Publications  A definition of the exterior derivative in terms of Lie derivatives, Proc. Amer. Math. Soc. 5 (1954) 902908.  
On the differentiability of isometries, Proc. Amer. Math. Soc. 8 (1957) 805808.  
A Global Formulation of the Lie Theory of Transformation Groups, Memoirs of the AMS #22(1957 ).  
On a class of transformation groups, (with A.M. Gleason), Amer. J. Math. 79 (1957),631648.  
Imbedding of compact, differentiable,transformation groups in orthogonal representations, J. Math. and Mech. 6 (1957), 674678.  
A covering homotopy theory and the classification of Gspaces, Proc. Nat. Acad. Sci.U.S.A. 45 (1959), 857859.  
Natural operations on differential forms, Trans. Amer. Math. Soc. 92 (1959),125141.  
Extending diffeomorphisms, Proc. Amer. Math. Soc. 11 (1960), 274277.  
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) 163178.  
The Classification of Gspaces, Memoirs of the Amer. Math. Soc. 36 (1960).  
On the cohomology of Lie rings, Proc. of Symposium on Differential Geometry, Tucson, Feb. 1960.  
On the local triviality of the restriction map for embeddings, Comm. Math. Helv. 34 (1960), 306312.  
Deformations of compact differentiable transformation groups, (with T. E. Stewart) Amer. J. Math. 82 (1960) 935937.  
Logarithmically exact differential forms, Proc. Amer. Math. Soc. 12 (1961), 5052.  
Torus bundles over tori, (with T. E. Stewart), Proc. Amer. Math. Soc. 12 (1961), 2640.  
On the existence of slices for actions of noncompact Lie groups, Annals of Math. 73 (1961), 295323.  
The cohomology of differentiable transformation groups, (with T. E. Stewart) Amer. J. Math. 83 (1961), 623644.  
Equivalence of nearly differentiable actions of a compact group, Bull. Amer. Math. Soc. 67 (1961), 362364.  
Morse theory on Hilbert manifolds, Topology 2 (1963), 299340.  
Uncountably many inequivalent actions of a compact group on R^n, (with R. Richardson), Proc. Amer. Math. Soc. 14 (1963), 374377.  
A generalized Morse theory, (with S. Smale), Research Announcement, Bull. Amer. Math. Soc. 70 (1964), 165172.  
Seminar on the AtiyahSinger Index Theorem, Annals of Math. Study No. 4 (1964).  
On the homotopy type of certain groups of operators, Topology 3 (1965) 271279.  
Homeomorphic conjugacy of automorphisms on the Torus, (with L. Adler), Proc. Amer. Math. Soc. 16 (1965) 12221225.  
Homotopy theory of infinite dimensional manifolds, Topology 5 (1966) 116.  
LusternikSchnirelman theory on Banach Manifolds Topology 5 (1966) 115132.  
Foundations of Global Nonlinear Analysis, Benjamin and Co. New York, 1968.  
The classification of real division algebras, Amer. Math. Monthly, 75, (1968 ) 366368  
Manifolds of sections of fiber bundles and the calculus of variations, Proc.Symp.on Nonlinear Analysis, vol. XVIII, Amer. Math. Soc.  
Critical point theory and the minimax principle, Proc. Symp. on Global Analysis, vol. XV, Amer. Math. Soc. 185212.  
The Morse Lemma for Banach spaces, Bull. Amer. Math. Soc. 75 (1969) 968971.  
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 Cinfinity actions, Amer. Jour. Math. 88 (1970) 748760.  
Banach manifolds of fiber bundle sections, Proc. International Cong. Math. Nice, 1970, vol. 2, 243249, 1971.  
Natural bundles have finite order, (with C. L. Terng), Topology, 16 (1977) 271277.  
A topological GaussBonnet theorem, Jour. of Diff. Geometry, 13 (1978) 385398.  
An analogue of Hartogs' theorem in an algebraic setting, Amer. Jour. Math. 100 (1978), 387406.  
The Principal of Symmetric Criticality, Comm. Math. Physics, 69 (1979) 1930.  
The Geometrization of Physics, TsingHua University Press, 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, 247301 (1984).  
Geometry and topology of isoparametric submanifolds, (with W. Y. Hsiang and C. L. Terng), (Research announcement), Proc. Nat. Acad. Sci. USA, 82(1985) 48634865.  
Reduction of variables for minimal submanifolds, (with C.L. Terng), Proc. Amer. Math. Soc., 98 (1986) 480484.  
A general canonical form theorem, (with C.L. Terng), Transactions Amer. Math. Soc., 300 (1987) 771789.  
Geometry of canonical forms, (with C.L. Terng), (Proceedings of the Kovaleskaya Symposium) Contemporary Mathematics, 64 (1987) 133151.  
Topology of isoparametric submanifolds (with W.Y. Hsiang and C.L. Terng), Jour. of Diff. Geometry, 27 (1988) 423460.  
Critical Point Theory and Submanifold Geometry (with C.L.Terng), Lecture Notes in Mathematics #1353,(280 pages) SpringerVerlag, NY (1988)  
The Life and Mathematics of ShiingShen Chern, in "ChernA Great Geometer of the Twentieth Century", edited by S.T. Yau, International Press, Hong Kong, 1992.  
Hyperpolar actions and kflat homogeneous spaces, (with E. Heintze, G. Thorbergsson, and C.L. Terng) J. reine angew. Math, 454 (1994) 163179  
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) 7798  
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) 214245  
The Symmetries of Solitons,Bull. Amer. Math. Soc. 34 (1997), 339403.  
The Visualization of Mathematics: Towards a Mathematical Exploratorium, Notices Amer. Math. Soc., 46, No.6 (JuneJuly 1999)  
A Simple Proof of the Banach Contraction Principle, The Journal for Fixed Point Theory and its Applications, 2 (2007) 221223  
Euler's Fixed Point Theorem: The Axis of a Rotation (with Bob Palais), The Journal for Fixed Point Theory and its Applications, 2 (2007) 215220  
Linear and Nonlinear Waves and Solitons, in The Princeton Companion to Mathematics, T. Gower Ed., Princeton Univ. Press 2008, 234239  
An Introduction to Ordinary Differential Equations and Classical Mechanics, (with Robert A. Palais) AMS STML51, ISBN10: 0821821385 (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 ) 892909  
Grant  The National Science Foundation DUE Award #0514781  
Professional Society 
AMS, MAA, ACM, AAAS 

Other Experience 
Professor of Mathematics Brandeis Univ. 1963—2003 

Link to this profile  http://www.faculty.uci.edu/profile.cfm?faculty_id=5158  
Last updated  06/13/2014  