
Karen Uhlenbeck
Professor Emeritus
Department of Mathematics
Sid W. Richardson Foundation Regents Chair in Mathematics #3Nonlinear Analysis, Gauge Theory and Integrable Systems

Ph.D., Brandeis University (1968)
Research Interests
Nonlinear Analysis, Gauge Theory and Integrable Systems
Geometric Partial Differential Equations, The Calculus of Variations, (especially scale invariant problems) Gauge Theory (now mostly for wave and nonlinear Schoedinger systems) Integrable Systems, Virasoro actions, Nonlinear waves and nonlinear Schroedinger Equations, (especially scale invariant problems).
I am a member of the geometry group in the mathematics department. The geometry group maintains a website with general and current information. http://www.ma.utexas.edu/users/plowrey/dev/
My recent research has been mainly on two subjects, with two groups of coauthors. I have written four papers of with ChuuLian Terng on the geometric aspects of integrable systems. With Andrea Nahmod and Atanas Stefanov I authored two papers on wave maps and Schoedinger maps. These are all posted on the LANL preprint server (in geometry or anaylsis).

Articles
Regularity Theorems for solutions of elliptic polynomial equations, Amer. Math. Soc., Symposium in Pure Math. XVI (1970), 225231.Morse theory on Banach manifolds, Bull. Amer. Math. Soc., 76(1970), 105107.
Integrals with nondegenerate critical points, Bull. Amer. Math. Soc., 76(1970), 125128.
Harmonic maps; a direct method in the calculus of variations, Bull. Amer. Math. Soc., 76(1970), 10821087.
Morse theory on Banach manifolds, J. Funct. Anal., 10(1972), 430445.
Bounded sets and Finsler structures of manifolds of maps, J. Diff. Geom., 7(1972), 589599.
Eigenfunctions of Laplace operators, Bull. Amer. Math. Soc., 78(1972), 107376.
Lorentz geometry, global analysis and its applications, Vol. 3, International Center for Theoretical Physics, Trieste (1972), 23542.
The Morse index theorem in Hilbert space, J. Diff. Geom., 8(1973), 555564.A new proof of a regularity theorem for elliptic systems, Proc. Amer. Math. Soc., 37(1973), 315316.
Morse theory for geodesics on a Lorentz manifold, Topology, 14(1975), 6990.
Generic properties of Eigenfunctions, Amer. J. Math., 98(1976), 10591078.
Regularity for a class of nonlinear elliptic equations, Acta Math., 48(1977), 217238.
(with J. Sacks) The existence of minimal immersions of twospheres, Bull. Amer. Math. Soc., 83(1977), 10331036.
Removeable singularities in YangMills fields, Bull. Amer. Math. Soc., 1(New Series, 1979), 112114.
(with J. Sacks) The existence of minimal immersions of 2spheres, Ann. of Math., 113(1981), 124.
Morse theory by perturbation methods with applications to harmonic maps, Trans. Amer. Math. Soc., 267(1981), 569583.
Variational problems for gauge fields, Seminar on Differential Geometry, S. T. Yau (ed.), Princeton University Press (1982), 455464.
Removeable singularities in YangMills fields, Comm. Math. Phys., 83(1982), 1129.
Connections with tex2html_wrap_inline212 bounds on curvature, Comm. Math. Phys., 83(1982), 3142.
Equivariant harmonic maps into spheres, Proceedings of the Tulane Conference on Harmonic Maps, Knill, Kalka and
Sealey (eds.), Lecture Notes in Mathematics 949, SpringerVerlag (1982), 146158.
(with J. Sacks) Minimal immersions of closed Riemann surfaces, Trans. Amer. Math. Soc., 271(1982), 639652.
(with R. Schoen) A regularity theory for harmonic maps, J. Diff. Geom., 17(1982), 307335.
Minimal spheres and other conformal variational problems, Seminar on Minimal Submanifolds, E. Bombieri (ed.),
Princeton University Press (1983), 169176.
Closed minimal surfaces in hyperbolic 3manifolds, Seminar on Minimal Submanifolds, E. Bombieri (ed.), Princeton
University Press (1983), 147168.
Boundary regularity and Dirichlet Problem for harmonic maps, J. Diff. Geom., 18(1983), 253268.
Conservation laws and their application in Global Differential Geometry, in Srinivasan and Sally (eds.), Emmy Noether in
Bryn Mawr (1983), SpringerVerlag, 103115.
Regularity of minimizing harmonic maps into spheres, Invent. Math., 78(1984).
Variational problems for Gauge fields, Proceedings of the International Congress of Mathematics, August 1624, 1983,
Warsaw (1984), 613619.
The Chern classes of Sobolev connections, Comm. Math. Phys., 101(1985), 449457.
(with S.T. Yau) On the existence of Hermitian YangMills connections in stable bundles, Comm. Pure Appl. Math., 39(1986), S257S297.
Commentary on Analysis in the Large, in A Century of Mathematics in America, Part II, Peter Duren (ed.), American Mathematical Society (1988), 357359.
Harmonic Maps into Lie Groups (classical solutions of the chiral model), J. Diff. Geom., 30 (1989), 150.
(with L. M. Sibner, R. J. Sibner) Solutions to YangMills Equations which are not selfdual, Proc. Nat. Acad. Sci., 89(1989), 86108613.
Applications of nonlinear analysis in topology, Proc. of the ICM90, Mathematical Society of Japan, 1991, 261279.
Instantons and their relatives, Mathematics into the 21st Century, Browder (ed.), American Mathematical Society (1992), 467479.
On the connection between harmonic maps and the selfdual YangMills and the SineGordon equations, J. Geom. Phys., 8(1992), 283316.
(with M. Atiyah, et al.) Responses to ``Theoretical Mathematics: Toward a Cultural Synthesis of Mathematics and Theoretical Physics'', by A. Jaffe and F. Quinn, Bull. Amer. Math. Soc. (new series), 30(1994), 201202.
(with G. Daskalopoulos) An application of traversality to the topology of the moduli space of stable bundles, Topology, 34(1995), 203215.
(with G. Daskalopoulos and R. Wentworth) Moduli of extensions of holomorphic bundles on KÃ¤hler manifolds, Comm. Anal. Geom, 3(1995), 479522.
Moduli spaces and adiabatic limits, Notices of the AMS, 42(1995), 4142.
(with R. Mazzeo and D. Pollack) Connected sum structions for constant scalar curvature metrics, Topological Methods in Nonlinear Analysis, 6(1995), 207233.
(with R. Mazzeo and D. Pollack) Moduli spaces of singular Yamabe metrics, J. Amer. Math. Soc., 9(1996), 303343.
(with C.L. Terng) Poisson Actions and Scattering Theory for Integrable Systems, Survey in Surveys in Differentiable Geometry, vol 4, International Press (l998).
(with C.L. Terng) Introduction to the volume "Survey's in Differential Geometry," Integrable Systems, Volume 4 (2000), 15.
(with C.L. Terng) The Geometry of Solitons (cover article) Notices of the AMS 47 (2000),1725.
(with C L Terng) Backlund Transformations and Loop Group Actions, Communications in Pure and Applied Mathematics 53 (2000, 175.
(with N.H. Chang and J. Shatah) Schroedinger Maps, Comm. Pure Appl. Math 53 (2000),590602.
(with J. Viaklovsky) Regularity of weak solutions to critical exponent variational problems, Mathematical Research Letters, I P, vol 7 no 56 (2000), 652656.
(with A. Nahmod and A. Stefanov) On the wellposedness of the wave map problem in high dimensions, Comm. Analysis and Geometry, vol 11, no 1 (2003) 2983.
(with A. Nahmod and A Stephanov) On Schroedinger Maps, Comm. Pure Appl. Math 56 (2003) no 1, 114151.
(with C.L. Terng) Wave maps into symmetric spaces, Comm. Anal. Geom. 12 (2004), no 12, 345388.
(with C. L. Terng) Schroedinger flows on Grassmannians, Integrable systems, geometry and topology, 234256, AMS/IP Stud. Adv.Math, AMS, Providence (2006), 235256.
(with M. Vajiac) Virasoro Actions on harmonic maps, submitted to JDG.
(with C. L. Terng) On Spacetime Monopoles.
(with A. Goncalves) On constant mean curvature embeddings of surfaces in space forms, To appear in CAG.
Books
(with D. Freed) Instantons and 4manifold Topology, Mathematical Sciences Research Institute Lecture Notes, 1, Springer Verlag, 1984.
(edited) Global Analysis in Modern Mathematics: a Symposium in Honor of Richard Palais' sixtieth birthday. Publish or Perish, 1993.
(edited with D. Freed) Geometry and Quantum Field Theory, American Mathematical Society, 1995.

 2007 Steele Prize, Amercian Mathematics Society
 2004 Honorary Degree: Doctor of Science; University of Michigan
 2001 National Medal of Science
 2001 Honaray Degree: Doctor Of Science: University of Ohio
 2000 National Medal of Science
 2000 Honorary Degree: Doctor of Science, University of Illinois, Champaign
 1995 CommonWealth Award for Science and Technology
 1988 Alumni Achievement Award, Brandeis University
 1988 Honorary Degree: Doctor of Science, Knox College, Illinois
 1986 National Academy of Sciences, Fellow
 1985 American Academy of Arts and Sciences, Fellow
 1984 Alumna of the Year, University of Michigan
 198388 MacArthur Prize Fellowship
 197980 Albert Einstein Fellow, Institute for Advanced Study, Princeton
 197476 Sloan Foundation Fellowship
 196468 National Science Foundation Graduate Fellowship
 196465 Woodrow Wilson Fellow
 1964 Phi Beta Kappa