Education

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

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
• 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)

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)

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)