CURRICULUM VITAE of Karen K. Uhlenbeck Updated December 8, 1996 Birthdate: August 24, 1942; Cleveland, Ohio Education: 1964 B. S. University of Michigan 1966 M.A. Brandeis University 1968 Ph.D. Brandeis University (PhD advisor: Richard Palais) Career: Principal Professional Positions: 1954-55 Assistant Professor, Florida State University 1955-56 Visiting Lecturer, University of Wisconsin 1956-59 Assistant Professor, Purdue University 1959-61 Associate Member, Institute for Advanced Study 1961-63 Assistant Professor, University of Chicago 1963-67 Associate Professor, Northwestern University 1967-87 Professor, Northwestern University 1987- Professor, The University of Texas, Austin Other Professional Positions and Honors: 1995 Member, Institute for Advanced Study 1992 Mathematics Institute, University of Warwick 1995,93,90 88, 75 Aspen Institute for Theoretical Physics 1989 IBM J.T. Watson Research Center 1987 Institute des Hautes Etudes Scientifique 1985 University of California, San Diego 1985 Instituto Matematica Pura y Applicado 1983 Boston University 1982 University of California, Berkeley 1972-73 Institute des Hautes Etudes Scientifique, Paris 1971 Instituto Matematica Pura y Applicada, Rio de Janeiro 1961-63 NSF Senior Postdoctoral Fellow, Member, Princeton Institute for Advanced Study Research Publications: 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, Ann. 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 Rn, (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, Ann. 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 principal, 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. U.S.-China Symp. on Differential Geometry and Differential Equations II, (1985). 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