Professor, and Sid W. Richardson Regents Chairholder, Department of Mathematics, University of Texas, Austin, US.
Geometric Partial Differential Equations
The Calculus of Variations, especially scale invariant problems (past interest)
Gauge Theory (now mostly for wave and non-linear Schoedinger systems)
Non-linear waves and non-linear Schroedinger Equations, especially scale invariant problems
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
1983-88 MacArthur Prize Fellowship
1979-80 Albert Einstein Fellow, Institute for Advanced Study, Princeton
1974-76 Sloan Foundation Fellowship
1964-68 National Science Foundation Graduate Fellowship
1964-65 Woodrow Wilson Fellow
1964 Phi Beta Kappa
Regularity Theorems for solutions of elliptic polynomial equations, Amer. Math. Soc., Symposium in Pure Math. XVI (1970), 225-231.
Morse theory on Banach manifolds, Bull. Amer. Math. Soc., 76(1970), 105-107.
Integrals with nondegenerate critical points, Bull. Amer. Math. Soc., 76(1970), 125-128.
Harmonic maps; a direct method in the calculus of variations, Bull. Amer. Math. Soc., 76(1970), 1082-1087.
Morse theory on Banach manifolds, J. Funct. Anal., 10(1972), 430-445.
Bounded sets and Finsler structures of manifolds of maps, J. Diff. Geom., 7(1972), 589-599.
Eigenfunctions of Laplace operators, Bull. Amer. Math. Soc., 78(1972), 1073-76.
Lorentz geometry, global analysis and its applications, Vol. 3, International Center for Theoretical Physics, Trieste (1972), 235-42.
The Morse index theorem in Hilbert space, J. Diff. Geom., 8(1973), 555-564.
A new proof of a regularity theorem for elliptic systems, Proc. Amer. Math. Soc., 37(1973), 315-316.
Morse theory for geodesics on a Lorentz manifold, Topology, 14(1975), 69-90.
Generic properties of Eigenfunctions, Amer. J. Math., 98(1976), 1059-1078.
Regularity for a class of non-linear elliptic equations, Acta Math., 48(1977), 217-238.
(with J. Sacks) The existence of minimal immersions of two-spheres, Bull. Amer. Math. Soc., 83(1977), 1033-1036.
Removeable singularities in Yang-Mills fields, Bull. Amer. Math. Soc., 1(New Series, 1979), 112-114.
(with J. Sacks) The existence of minimal immersions of 2-spheres, Ann. of Math., 113(1981), 1-24.
Morse theory by perturbation methods with applications to harmonic maps, Trans. Amer. Math. Soc., 267(1981), 569-583.
Variational problems for gauge fields, Seminar on Differential Geometry, S. T. Yau (ed.), Princeton University Press (1982), 455-464.
Removeable singularities in Yang-Mills fields, Comm. Math. Phys., 83(1982), 11-29.
Connections with tex2html_wrap_inline212 bounds on curvature, Comm. Math. Phys., 83(1982), 31-42.
Equivariant harmonic maps into spheres, Proceedings of the Tulane Conference on Harmonic Maps, Knill, Kalka and Sealey (eds.), Lecture Notes in Mathematics 949, Springer-Verlag (1982), 146-158.
(with J. Sacks) Minimal immersions of closed Riemann surfaces, Trans. Amer. Math. Soc., 271(1982), 639-652.
(with R. Schoen) A regularity theory for harmonic maps, J. Diff. Geom., 17(1982), 307-335.
Minimal spheres and other conformal variational problems, Seminar on Minimal Submanifolds, E. Bombieri (ed.), Princeton University Press (1983), 169-176.
Closed minimal surfaces in hyperbolic 3-manifolds, Seminar on Minimal Submanifolds, E. Bombieri (ed.), Princeton University Press (1983), 147-168.
Boundary regularity and Dirichlet Problem for harmonic maps, J. Diff. Geom., 18(1983), 253-268.
Conservation laws and their application in Global Differential Geometry, in Srinivasan and Sally (eds.), Emmy Noether in Bryn Mawr (1983), Springer-Verlag, 103-115.
Regularity of minimizing harmonic maps into spheres, Invent. Math., 78(1984).
Variational problems for Gauge fields, Proceedings of the International Congress of Mathematics, August 16-24, 1983, Warsaw (1984), 613-619.
The Chern classes of Sobolev connections, Comm. Math. Phys., 101(1985), 449-457.
(with S.-T. Yau) On the existence of Hermitian Yang-Mills connections in stable bundles, Comm. Pure Appl. Math., 39(1986), S257-S297.
Commentary on Analysis in the Large, in A Century of Mathematics in America, Part II, Peter Duren (ed.), American Mathematical Society (1988), 357-359.
Harmonic Maps into Lie Groups (classical solutions of the chiral model), J. Diff. Geom., 30 (1989), 1-50.
(with L. M. Sibner, R. J. Sibner) Solutions to Yang-Mills Equations which are not self-dual, Proc. Nat. Acad. Sci., 89(1989), 8610-8613.
Applications of non-linear analysis in topology, Proc. of the ICM-90, Mathematical Society of Japan, 1991, 261-279.
Instantons and their relatives, Mathematics into the 21st Century, Browder (ed.), American Mathematical Society (1992), 467-479.
On the connection between harmonic maps and the self-dual Yang-Mills and the Sine-Gordon equations, J. Geom. Phys., 8(1992), 283-316.
(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), 201-202.
(with G. Daskalopoulos) An application of traversality to the topology of the moduli space of stable bundles, Topology, 34(1995), 203-215.
(with G. Daskalopoulos and R. Wentworth) Moduli of extensions of holomorphic bundles on KÃ¤hler manifolds, Comm. Anal. Geom, 3(1995), 479-522.
Moduli spaces and adiabatic limits, Notices of the AMS, 42(1995), 41-42.
(with R. Mazzeo and D. Pollack) Connected sum structions for constant scalar curvature metrics, Topological Methods in Nonlinear Analysis, 6(1995), 207-233.
(with R. Mazzeo and D. Pollack) Moduli spaces of singular Yamabe metrics, J. Amer. Math. Soc., 9(1996), 303-343.
(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), 1-5.
(with C.L. Terng) The Geometry of Solitons (cover article) Notices of the AMS 47 (2000),17-25.
(with C L Terng) Backlund Transformations and Loop Group Actions, Communications in Pure and Applied Mathematics 53 (2000, 1-75.
(with N.H. Chang and J. Shatah) Schroedinger Maps, Comm. Pure Appl. Math 53 (2000),590-602.
(with J. Viaklovsky) Regularity of weak solutions to critical exponent variational problems, Mathematical Research Letters, I P, vol 7 no 5-6 (2000), 652-656.
(with A. Nahmod and A. Stefanov) On the well-posedness of the wave map problem in high dimensions, Comm. Analysis and Geometry, vol 11, no 1 (2003) 29-83.
(with A. Nahmod and A Stephanov) On Schroedinger Maps, Comm. Pure Appl. Math 56 (2003) no 1, 114-151.
(with C.L. Terng) Wave maps into symmetric spaces, Comm. Anal. Geom. 12 (2004), no 1-2, 345-388.
(with C. L. Terng) Schroedinger flows on Grassmannians, Integrable systems, geometry and topology, 234-256, AMS/IP Stud. Adv.Math, AMS, Providence (2006), 235-256.
(with M. Vajiac) Virasoro Actions on harmonic maps, submitted to JDG.
(with C. L. Terng) On Space-time Monopoles.
(with A. Goncalves) On constant mean curvature embeddings of surfaces in space forms, To appear in CAG.
(with D. Freed) Instantons and 4-manifold 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.