Curriculum Vitae

Robert L Bryant

17 Gauss Way
Berkeley, CA 94720-5070 		(510) 642-0143 (office)
(email)
Personal

Born: 1953
Place: Kipling, NC
Citizenship: US

Education

PhDUniversity of North Carolina at Chapel Hill1979
BSNorth Carolina State University at Raleigh1974
Areas of Research

Nonlinear Partial Differential Equations and Differential Geometry

Areas of Interest

exterior differential systems
differential geometry
algebraic geometry
Finsler geometry

Areas of Experience

Geometric Partial Differential Equations
Differential Geometry

Professional Experience / Employment History

Mathematical Sciences Research Institute
Director, , August 01, 2007 - present
University of California at Berkeley
Professor, Mathematics, July 01, 2007 - present
Duke University
J. M. Kreps Professor, Mathematics, 1988-present
Arts and Sciences Professor, Mathematics, 1987-88
Rice University
Noah Harding Professor, Mathematics, 1986-88
Professor, Mathematics, 1982-86
Associate Professor, Mathematics, 1981-82
Assistant Professor, Mathematics, 1979-81
Visiting Positions
Nachdiplom Lecturer, Eidgenössische Technische Hochschule Zürich (ETH-Z), November 6, 2006 - December 22, 2006
Samuel Eilenberg Professor, Columbia University, January-April 2004
Simons Research Professor, Mathematical Sciences Research Institute, August-December 2003
Clay Research Professor, Mathematical Sciences Research Institute, January-May 2002
Senior Visitor, Mathematical Sciences Research Institute, August-December 2001
Professor, Institute Elie Cartan, June 1998
Visitor, Instituto Nacional de Matematica Pura e Applicada, July-August 1996
Visitor, Nankai Institute of Mathematics, May 1995
Andre Aisenstadt Professor, Centre de Recherches Mathematique, October 1994
Member, Mathematical Sciences Research Institute, January-June 1994
Director's Visitor, Institute for Advanced Study, September-December 1993
Visitor, University of Adelaide, July-August 1993
Member, Instituto Nacional de Matematica Pura e Applicada, July-August 1990
W. R. Reynolds Professor, University of North Carolina at Chapel Hill, July-December 1987
Member, Instituto Nacional de Matematica Pura e Applicada, May 1986
Member, Institue des Hautes Etudes Scientifiques, November 1985
Member, Max Planck Institut, October 1985
Professor, Duke University, August-December 1984
Member, Mathematical Sciences Research Institute, April-May 1983
Associate Professor, Harvard, August-December 1982
Member and NSF Postdoctoral Fellow, Institute for Advanced Study, 1979-80
Awards, Honors, and Distinctions

NSF Postdoctoral Research Fellow 1979--80
Alfred P. Sloan Fellow 1982--84
Presidential Young Investigator 1984--89
Trinity College Distinguished Teaching 1992
MAA Southeastern Region Distinguished Teaching 1993
Fellow of the American Academy of Arts and Sciences 2002--
Member, National Academy of Sciences, 2007--
Member, Phi Beta Kappa, 2007--
Distinguished Alumni Award from the College of Physical and Mathematical Sciences, NCSU Alumni Association, November 2005

Major Grant Support

DMS-8352009
DMS-8601853
DMS-8905207
DMS-8996110
DMS-9205222
DMS-9505125
DMS-9870164 (current)
DMS-0103884 (current)

Recent Grant Support

Conferences Organized

Member of Organizing Board, Annual East Coast Geometry Festival, 1 January 1990  
Conference Organizer, Workshop on Calibrations, June 26, 2006 - June 30, 2006  
Scientific Advisor on Organizing Committee, Singularities in Analysis, Geometry, and Topology: A Conference Honoring the Retirements of F. Reese Harvey and John Polking, November 11, 2005 - November 13, 2005  
Member of organizing committee, International Symposium on Finsler Geometry, August 10, 2004 - August 14, 2004  
co-Organizer, Oberwolfach Bi-Annual Differential Geometry in the Large, June 15, 2001 - May 31, 2004  
co-Organizer, MSRI Year-Long Program in Geometry (2003-2004), 2001-04  
Professional Service

University Committee
Director (since 2000), Chamber Arts Society of Durham, 1 September 1997  
Faculty Representative, Harassment Grievance Board, July 01, 2005 - June 30, 2008  
Member, Athletic Council Review Commitee, September, 2006 - December, 2006  
Member (1st year), Chair (2nd year), Provost's Advisory Committee on Distinguished Professorships, September, 2004 - August, 2006  
Member, Duke Academic Priorities Committee, Duke, 1999-2003  
Committee member, Search Committee for Director of Program in Education, Duke University, 2002-03  
Member, Duke Harrassment Grievance Board, 1998-2000  
Committee Member, Bass Chair Advisory Committee, 1997-99  
Member, Duke Curriculum Review Committee, 1997-99  
Member, Provost's Advisory Committee on AP&T, 1995-98  
Papers Refereed
Refereed for a number of journals, November 2006  
Reviewed propoals, November 2006  
Referee, Refereed for a number of journals, January 01, 2005 - December 31, 2005  
reviewer, Refereed for a number of journals, January 01, 2004 - December 31, 2004  
Referee, Refereeing papers, January-December 2002  
Refereeing papers, January-December 2001  
Reviewer, Reviewed manuscripts, January-December 2000  
Math Community Services
Member, Communications in Analysis and Geometry Editorial Board, 27 November 2002  
Member, Differential Geometry and its Applications Editorial Board, 1 May 1999  
Member, Duke Mathematical Journal Editorial Board, 1 July 1997  
Vice President, American Mathematical Society, February 01, 2007 - January 31, 2010  
Member, AMS Editorial Boards Committee, February 01, 2006 - January 31, 2009  
Associate Editor, Jounal of the American Mathematical Society, February 01, 2005 - January 31, 2008  
Director, Park City/IAS Mathematics Institute, January, 2007  
Executive Committee Member, American Mathematical Society Council, 2000-04  
Member, Harvard Board of Visitors, Harvard University, 2001-04  
Council Member at Large, Council of the American Mathematical Society, January 1, 1999 - March 31, 2004  
Chair, Mathematical Sciences Research Institute Board of Trustees, March 1, 2001 - March 1, 2004  
Member (Years 1&2), Chair (Years 3-6), AMS Committee on Publications, 1998-2004  
Southeastern Section Lecturer, Mathematical Association of America, 2001-03  
Member, Mathematical Sciences Research Institute Board of Trustees, March 19, 1999 - February 28, 2001  
Director of the Undergraduate Program, IAS/Park City Mathematics Institute, 1993-2000  
Panel Member of Proposal Evaluators, Fundacao para a Ciencia e Tecnologia (FCT), February-June 2000  
Member, AMS Task Force on Membership, 1998-2000  
Editor, Transactions of the American Mathematical Society, 1992-97  
Other
Academic member of the board of directors, The Vietnam Education Foundation, 2002-05  
Selected Recent Invited Talks

Riemannian Submersions as PDE, MSRI, May 05, 2008  
Riemannian Submersions as PDE, Duke University, April 25, 2008  
The Hessian representation problem, University of Pennsylvania, April 24, 2008  
Geometric flows and special holonomy, University of Pennsylvania, April 23, 2008  
The unreasonable effectiveness of geometric methods, University of Pennsylvania, April 22, 2008  
Riemannian Submersions as PDE, University of California, Irvine, February 02, 2008  
New results in Riemannian submersions from space forms, CIRM, Luminy France, November 28, 2007  
Minimizing cycles in compact simple Lie groups, University of California at Berkeley, October 28, 2007  
A heat flow for unimodular CR hypersurfaces, Columbia University, October 04, 2007  
A flow for real hypersurfaces in unimodular complex surfaces, Universitat Tübingen, Germany, December 18, 2006  
On the geometry of almost-complex 6-manifolds, Oxford University, Oxford, UK, December 04, 2006  
A flow for real hypersurfaces in unimodular complex surfaces, Imperial College, London, UK, December 01, 2006  
Aufwiedersehen Surfaces, Revisited, Technische Universitat - Berlin, November 24, 2006  
Real hypersurfaces in unimodular complex surfaces, Technische Universitat - Berlin, November 23, 2006  
The idea of holonomy and its current development, Zurich Mathematics Colloquium (at ETH-Zurich), November 14, 2006  
Closed Sp(2)Sp(1) structures on 8-manifolds, University of New Mexico, Albuquerque, October 11, 2006  
Some nonembedding and nonextension results in special holonomy, Consejo Superior de Investigaciones Científicas, Madrid Spain, September 04, 2006  
Aufwiedersehen Surfaces, Revisited, Madrid, Spain, August 25, 2006  
Geometry of Almost Complex 6-manifolds, International Conference on Differential Geometry, Münster, Germany, August 15, 2006  
The idea of holonomy, Park City, Utah, July 14, 2006  
Gradient Kahler Ricci solitons, Johns Hopkins University, April 27, 2006  
Aufwiedersehen Surfaces, Revisited, Johns Hopkins University, April 25, 2006  
Aufwiedersehen Surfaces, Revisited, College of Charleston, Charleston, SC, April 13, 2006  
Calibrations in Geometry and Topology, Colorado University at Boulder, CO, March 17, 2006  
Real hypersurfaces in unimodular complex surfaces, Texas A&M Department of Mathematics, February 20, 2006  
Finsler spheres of constant curvature, Texas Geometry and Topology Conference, University of Houston, February 19, 2006  
Equi-Poisson sequences in the plane, SGS VIII: Georgia Institute of Technology, December 19, 2005  
The classification of reversible Finsler metrics on the 2-sphere with constant flag curvature, "On Finsler geometry" workshop. CIRM Luminy, France, November 18, 2005  
Projective equivalence of Finsler metrics of constant curvature, "On Finsler geometry" workshop. CIRM Luminy, France, November 17, 2005  
The local structure of Finsler metrics of constant flag curvature, "On Finsler geometry" workshop. CIRM Luminy, France, November 16, 2005  
Resolving a coassociative singularity, `Singularities in geometry and analysis', a conference in honor of F. Reese Harvey and John Polking, Rice University, Houston, TX, November 13, 2005  
The geometry of almost complex 6-manifolds, Nara University, Nara Japan, October 29, 2005  
The geometry of real hypersurfaces in complex unimodular surfaces, RIMS, Kyoto Japan, October 24, 2005  
A flow for CR hypersurfaces in unimodular surfaces, Mathematiches ForschungsInstitut Oberwolfach, August 08, 2005  
Real hypersurfaces in unimodular complex surfaces, Universidade Federal do Rio de Janeiro, August 04, 2005  
Surfaces with prescribed shape operator, Universidade da Brasília, August 03, 2005  
Second order families of special Lagrangian 3-folds, Universidade da Brasília, August 02, 2005  
Real hypersurfaces in unimodular complex surfaces, Universidade da Brasília, August 01, 2005  
A survey of Finsler surface theory, IMPA, Rio de Janeiro, Brazil, July 28, 2005  
Calculations with G_2-structures, Gokova, Turkey, June 03, 2005  
Extension results for calibrations and special holonomy, Gokova, Turkey, May 30, 2005  
Existence and uniqueness for gradient Kahler-Ricci solitons, Ecole Polytechnique, Palaiseau, France, May 19, 2005  
A flow for CR hypersurfaces in unimodular surfaces, Columbia University, May 02, 2005  
Finsler 2-spheres of constant curvature, Southeast Geometry Seminar VII, Emory University, March 16, 2005  
MAA Short Course on Geometry and the Calculus of Variations, MAA Southeastern 84th Meeting at Meredith College, March 11, 2005  
Aufwiedersehen Surfaces, Revisited, UNC Chapel Hill Department of Mathematics, January 27, 2005  
Calibrations in Geometry and Topology, Institute for Advanced Study, Princeton, NJ, October 22, 2004  
Gradient Kahler Ricci solitons, Second Yamabe Memorial Symposium (U-Minn), September 18, 2004  
Geodesically reversible Finsler spheres with K=1, Nankai Institute of Mathematics, Tianjin, PRC, August 11, 2004  
Gradient Ricci solitons, Program in Riemannian Geometry, University of Montreal, July 14, 2004  
The gometry and topology of G_2 and Spin(7) structures, "Strings at Snowbird" (AMS Summer Workshop at Snowbird, UT), June 6-11, 2004  
Gradient Kahler Ricci solitons, Gokova, Turkey (11'th annual Gokova Geometry/Topology Conf.), May 27, 2004  
Introduction to G_2 geometry I, II, Gokova, Turkey (11'th annual Gokova Geometry/Topology Conf.), May 24, 2004  
Aufwiedersehn Surfaces, Revisited, University of Wisconsin at Madison, May 07, 2004  
Singular reduction in special Lagrangian geometry and almost complex geometry, Princeton University, May 05, 2004  
See Ya Later Surfaces, Brooklyn Polytechnic University, April 28, 2004  
Aufwiedersehn Surfaces, Revisited, University of Rochester, April 27, 2004  
Aufwiedersehn Surfaces, Revisited, University of Pennsylvania, April 14, 2004  
Singular PDE arising in special Lagrangian geometry, University of Pennsylvania, April 13, 2004  
Aufwiedersehn Surfaces, Revisited, Lehigh University, April 07, 2004  
The Poincaré Conjecture and Ricci Flow, University of Colorado at Boulder, March 30, 2004  
Some singular PDE arising in special Lagrangian geometry, University of Arkansas in Fayetteville, March 27, 2004  
Calibrations and inverse problems in the calculus of variations, Stanford University Colloquium, 13 November 2003  
Closed G_2 structures, UC-Irvine, 4 November 2003  
One hundred years of holonomy, Washington University in St. Louis, 5 October 2003  
One Hundred Years of Holonomy, UC-Berkeley, 29 September 2003  
Closed G2 structures, AMS-MSRI von Neumann Symposium, 2 September 2003  
Four Lectures on Manifolds with Special Holonomy, AMS-MSRI von Neumann Symposium, 11 August 2003  
Path geometry, Finsler metrics and exotic holonomy, BIRS Workshop on Differential Invariants and Invariant Differential Equations, 19 July 2003  
Resolving a coassociative cone, BIRS Workshop: Perspectives in Differential Geometry, 12 July 2003  
Six Lectures on Connections and Holonomy, von Neumann Preparatory Workshop in Banff, 21 June 2003  
Finsler metrics of constant flag curvature, Dartmouth University Seventh Annual Kemeny Lectures, 15 May 2003  
New Zoll metrics on the 2-sphere, Dartmouth University Seventh Annual Kemeny Lectures, 13 May 2003  
Geometry Old and New: From Euclid to String Theory, Dartmouth University Seventh Annual Kemeny Lectures, 12 May 2003  
Remarks on associative submanifolds, IPAM conference "Geometry and Physics of G2 manifolds", 29 April 2003  
The generality of Finsler metrics of constant flag curvature and some exotic holonomy groups, Massachusetts Institute of Technology, 24 February 2003  
Geometry New and Old: From Euclid to String Theory, Francis Marion University, Florence SC, 21 February 2003  
Does V - E + F = 2?, High Point University, High Point, NC, 12 February 2003  
Modern Differential Geometry, I & II, Howard University, Washington, DC, 21 September 2002  
Rigidity of cycles in Hermitian symmetric spaces, EDGE Conference at the University of Edinburgh, 2 August 2002  
Three Lectures on Exterior Differential Systems in Geometry, EDGE Summer School and Conference at the University of Edinburgh, 23 July 2002  
The generality of Finsler metrics of constant flag curvature and some exotic holonomy groups, MSRI Workshop on Finsler Geometry, 7 June 2002  
Moduli and Rigidity of Algebraic Cycles in Hermitian Symmetric Spaces, SUNY-Stony Brook Conference "Minimal Varieties in Geometry and Physics", 3 June 2002  
Calibrations and Exterior Differential Systems, Harvard University, 4 May 2002  
Calibrations and Exterior Differential Systems, UC Santa Barbara Mathematics Department, 25 April 2002  
De/Prescribing the Shape of a Surface, UC Santa Cruz Mathematics Department, 23 April 2002  
Three remarks about special Lagrangian geometry in dimension 3, Indiana University at Bloomington, 14 April 2002  
Finsler Geometry and the Calculus of Variations, Indiana University at Bloomington, 12 April 2002  
Minimizing cycles in compact simple Lie groups, Indiana University at Bloomington, 11 April 2002  
Complex geometry and Finsler metrics of constant positive flag curvature, Stanford University, 28 November 2001  
Three remarks on special Lagrangian 3-cycles, Special Session at AMS Regional meeting at UC-Irvine, 9-10 Nov 01, 11 November 2001  
Doctoral Theses Directed

Dan Fox, Second order families of coassociative submanifolds, (May 1, 2002 - May 20, 2005)  
Marianty Ionel, Second order families of special Lagrangian4-folds in C4, (2002)  
Chris Moseley (UNC), The geometry of sub-Riemannian Engel 4-manifolds, (2001)  
Sung Ho Wang, Legendrian submanifold path geometry, (2001)  
Ben McKay, Duality and integrable systems of pseudoholomorphic curves, (1999)  
Chris Michael, Uniqueness of calibrated cycles using exterior differential systems, (1996)  
Kevin Foltinek, Quasilinear third-order scalar evolution equations and their conservation laws, (1996)  
Jeanne Clelland, Geometry of conservation laws for a class of parabolic PDE, (1996)  
Keener Hughen, The sub-Riemannian geometry of three-manifolds, (1995)  
Thomas A. Ivey, On solitons for the Ricci flow, (1992)  
Lucas Hsu, Calculus of variations via the Griffiths formalism, (1991)  
Robert C. McLean, Deformations and moduli of calibrated submanifolds, (1990)  
J. M. Landsberg, Minimal submanifolds defined by first order systems of PDE, (1990)  
Tim Murdoch (Rice), Twisted calibrations and the cone on the Veronese surface, (1988)  
Steven Van Wilkinson (Rice), Characterizing Gauss maps, (1984)  
Professional Affiliations

American Mathematical Society
Mathematical Association of America
Chamber Arts Society of Durham (Director emeritus)

Publications

Books

  1. with David Bao, S.-S. Chern, Zhongmin Shen, eds., A sampler of Riemann-Finsler geometry, Mathematical Sciences Research Institute Publications, edited by Bao, David and Bryant, Robert L. and Chern, Shiing-Shen, vol. 50 (2004), pp. xii+363, Cambridge University Press, Cambridge
  2. with Phillip Griffiths and Dan Grossmann, Exterior Differential Systems and Euler-Lagrange Partial Differential Equations, Chicago Lectures in Mathematics (2003), University of Chicago Press (vii+213 pages, ISBN: 0-226-07794-2.)
  3. Selected works of Phillip A. Griffiths with commentary. Part 4. Differential systems., edited by R. L. Bryant and David R. Morrison (2003), American Mathematical Society, Providence, RI; International Press, Somerville, MA
  4. Rigidity and quasi-rigidity of extremal cycles in Hermitian symmetric spaces, Annals of Mathematics Studies (to appear)
  5. with S.-S. Chern, Robert B. Gardner, Hubert L. Goldschmidt,and Phillip A. Griffiths, Exterior Differential Systems, MSRI Publications18. Springer-Verlag, New York, 1991
  6. with Victor Guillemin, Sigurdur Helgason, and R. O. Wells, Jr. (eds.), Integral Geometry, Proceedings of the AMS-IMS-SIAM joint summer research conference held in Brunswick, Maine, August 12--18, 1984, pp. x+350, 1987, American Mathematical Society,
  7. with Marcel Berger and Chao Hao Gu (eds.), Differential Geometry and Differential Equations, Proceedings of the sixth symposium held at Fudan University, Shanghai, June 21--July 6, 1985, pp. xii+243, 1987, Springer-Verlag, Berlin

Papers Published

  1. with G. Manno, V. Matveev, A solution of a problem of Sophus Lie: Normal forms of 2-dimensional metrics admitting two projective vector fields, Mathematische Annalen, vol. 340 no. 2 (Spring, 2008), pp. 437--463
  2. Geodesically reversible Finsler 2-spheres of constant curvature, in Inspired by S. S. Chern---A Memorial Volume in Honor of a Great Mathematician, Nankai Tracts in Mathematics, edited by P. A. Griffiths, vol. 11 (Winter, 2006), World Scientific
  3. On the geometry of almost complex 6-manifolds, The Asian Journal of Mathematics, vol. 10 no. 3 (September, 2006), pp. 561--606
  4. Conformal geometry and 3-plane fields on 6-manifolds, in Developments of Cartan Geometry and Related Mathematical Problems, RIMS Symposium Proceedings, vol. 1502 (July, 2006), pp. 1-15, Kyoto University
  5. SO(n)-invariant special Lagrangian submanifolds of C^{n+1} with fixed loci, Chinese Annals of Mathematics, Series B, vol. 27 no. 1 (January, 2006), pp. 95--112
  6. Second order families of special Lagrangian 3-folds, in Perspectives in Riemannian Geometry, CRM Proceedings and Lecture Notes, edited by Vestislav Apostolov, Andrew Dancer, Nigel Hitchin, and McKenzie Wang, vol. 40 (2006), American Mathematical Society
  7. Some remarks on G2 structures, in Proceeding of Gökova Geometry-Topology Conference 2005, edited by S. Akbulut, T Önder, and R.J. Stern (2006), International Press
  8. Geometry of manifolds with special holonomy: "100 years of holonomy", in 150 years of mathematics at Washington University in St. Louis, Contemporary Mathematics, vol. 395 (2006), pp. 29--38, AMS
  9. Holonomy and Special Geometries, in Dirac Operators: Yesterday and Today, Conference Proceedings and Lecture Notes in Geometry and Topology, edited by Bourguignon, Branson, Chamseddine, Hijazi, and Stanton (2005), pp. 71-90, International Press (Proceedings of the Summer School and Workshop at CAMS- AUB, Lebanon, August 27 -- September 7, 2001.)
  10. with Edelsbrunner, Herbert and Koehl, Patrice and Levitt, Michael, The area derivative of a space-filling diagram, Discrete \& Computational Geometry. An International Journal of Mathematics and Computer Science, vol. 32 no. 3 (2004), pp. 293--308 (ISSN: 0179-5376.)
  11. Some remarks on Finsler manifolds with constant flag curvature, Houston Journal of Mathematics, vol. 28 no. 2 (2002), pp. 221–262
  12. Levi-flat minimal hypersurfaces in two-dimensional complex space forms, in Lie groups, geometric structures and differential equations---one hundred years after Sophus Lie (Kyoto/Nara, 1999), Adv. Stud. Pure Math., vol. 37 (2002), pp. 1–44, Math. Soc. Japan
  13. Bochner-Kähler metrics, Journal of the AMS, vol. 14 no. 3 (2001), pp. 623–715
  14. On surfaces with prescribed shape operator, Results in Mathematics, vol. 40 no. 1–4 (2001), pp. 88–121 (Dedicated to Shiing-Shen Chern on his 90th birthday.)
  15. Harmonic morphisms with fibers of dimension one, Communications in Analysis and Geometry, vol. 8 no. 2 (2000), pp. 219–265
  16. Recent advances in the theory of holonomy, Astérisque, vol. 266 no. 5 (2000), pp. 351–374 (Exposé No. 861.)
  17. Élie Cartan and geometric duality, in Journées Élie Cartan 1998 et 1999, vol. 16 (2000), pp. 5–20, Institut Élie Cartan
  18. Calibrated embeddings in the special Lagrangian and coassociative cases, Annals of Global Analysis and Geometry, vol. 18 no. 3–4 (2000), pp. 405–435 (Special issue in memory of Alfred Gray (1939--1998).)
  19. Pseudo-Riemannian metrics with parallel spinor fields and vanishing Ricci tensor, in Global Analysis and Harmonic Analysis, Séminaires & Congrès, vol. 4 (2000), pp. 53–93
  20. with Eric Sharpe, D-branes and Spinc-structures, Phys. Lett. B, vol. 450 no. 4 (1999), pp. 353–357
  21. Some examples of special Lagrangian tori, Adv. Theor. Math. Phys., vol. 3 no. 1 (1999), pp. 83–90
  22. Russell, Thomas and Farris, Frank, Integrability, Gorman systems, and the Lie bracket structure of the real line (with an appendix by –––), J. Math. Econom., vol. 29 no. 2 (1998), pp. 183–209
  23. Projectively flat Finsler 2-spheres of constant curvature, Selecta Math. (N.S.), vol. 3 no. 2 (1997), pp. 161–203
  24. On extremals with prescribed Lagrangian densities, in Manifolds and geometry (Pisa, 1993), Symposia Mathematica, edited by Paolo de Bartolomeis, Franco Tricerri and Edoardo Vesentini, vol. XXXVI (1996), pp. 86–111, Cambridge Univ. Press, Cambridge
  25. Classical, exceptional, and exotic holonomies: a status report, in Actes de la Table Ronde de Géométrie Différentielle (Luminy, 1992), Sémin. Congr., vol. 1 (1996), pp. 93–165, Soc. Math. France, Paris
  26. Finsler structures on the 2-sphere satisfying K=1, in Finsler geometry (Seattle, WA, 1995), Contemporary Mathematics, edited by David Bao, Shiing-shen Chern and Zhongmin Shen, vol. 196 (1996), pp. 27–41, Amer. Math. Soc., Providence, RI
  27. with Phillip Griffiths, Characteristic cohomology of differential systems, I: General theory, J. Amer. Math. Soc., vol. 8 no. 3 (1995), pp. 507–596
  28. with Phillip Griffiths, Characteristic cohomology of differential systems, II: Conservation laws for a class of parabolic equations, Duke Math. Journal, vol. 78 no. 3 (1995), pp. 531–676
  29. with Phillip A. Griffiths and Lucas Hsu, Hyperbolic exterior differential systems and their conservation laws, Part I, Selecta Math. (N.S.), vol. 1 no. 1 (1995), pp. 21–112
  30. with Phillip A. Griffiths and Lucas Hsu, Hyperbolic exterior differential systems and their conservation laws, Part II, Selecta Math. (N.S.), vol. 1 no. 2 (1995), pp. 265–323
  31. with Phillip Griffiths and Lucas Hsu, Toward a geometry of differential equations, in Geometry, Topology, & Physics, Conf. Proc. Lecture Notes Geom. Topology, edited by S.-T. Yau, vol. IV (1995), pp. 1–76, Internat. Press, Cambridge, MA
  32. with Robert B. Gardner, Control structures, in Geometry in nonlinear control and differential inclusions (Warsaw, 1993), Banach Center Publications, edited by Bronis\l aw Jakubczyk, Witold Respondek and Tadeusz Rze\.zuchowski, vol. 12 (1995), pp. 111–121, Polish Acad. Sci., Warsaw
  33. An introduction to Lie groups and symplectic geometry, in Geometry and quantum field theory (Park City, UT, 1991), IAS/Park City Mathematics, vol. 1 (1995), pp. 5–181, Amer. Math. Soc., Providence, RI
  34. with Lucas Hsu, Rigidity of integral curves of rank 2 distributions, Invent. Math., vol. 114 no. 2 (1993), pp. 435–461
  35. Two exotic holonomies in dimension four, path geometries, and twistor theory, in Complex geometry and Lie theory (Sundance, UT, 1989), Proc. Sympos. Pure Math., edited by James A. Carlson, C. Herbert Clemens and David R. Morrison, vol. 53 (1991), pp. 33–88, Amer. Math. Soc., Providence, RI
  36. Some remarks on the geometry of austere manifolds, Bol. Soc. Brasil. Mat. (N.S.), vol. 21 no. 2 (1991), pp. 133–157
  37. with Simon Salamon, On the construction of some complete metrics with exceptional holonomy, Duke Math. J., vol. 58 no. 3 (1989), pp. 829–850
  38. with F. Reese Harvey, Submanifolds in hyper-Kähler geometry, J. Amer. Math. Soc., vol. 2 no. 1 (1989), pp. 1–31
  39. Surfaces in conformal geometry, in The mathematical heritage of Hermann Weyl (Durham, NC, 1987), Proc. Sympos. Pure Math., vol. 48 (1988), pp. 227–240, Amer. Math. Soc., Providence, RI
  40. Surfaces of mean curvature one in hyperbolic space, in Théorie des variétés minimales et applications (Palaiseau, 1983–1984), Astérisque, vol. 154-155 (1987) (1988), pp. 321–347, Société Mathématique de France, Paris
  41. On notions of equivalence of variational problems with one independent variable, in Differential geometry: the interface between pure and applied mathematics (San Antonio, Tex., 1986), Contemporary Mathematics, edited by Mladen Luksic, Clyde Martin and William Shadwick, vol. 68 (1987), pp. 65–76, Amer. Math. Soc., Providence, RI
  42. A survey of Riemannian metrics with special holonomy groups, in Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Berkeley, Calif., 1986), (1987), pp. 505–514, Amer. Math. Soc., Providence, RI
  43. Metrics with exceptional holonomy, Ann. of Math. (2), vol. 126 no. 3 (1987), pp. 525–576
  44. Minimal Lagrangian submanifolds of Kähler-Einstein manifolds, in Differential geometry and differential equations (Shanghai, 1985), Lecture Notes in Math., edited by Chao Hao Gu, Marcel Berger and Robert L. Bryant, vol. 1255 (1987), pp. 1–12, Springer-Verlag, Berlin
  45. with Phillip Griffiths, Reduction for constrained variational problems and $\int{1\over 2}k\sp 2\,ds$, Amer. J. Math., vol. 108 no. 3 (1986), pp. 525–570
  46. Lie groups and twistor spaces, Duke Math. J., vol. 52 no. 1 (1985), pp. 223–261
  47. Minimal surfaces of constant curvature in Sn, Trans. Amer. Math. Soc., vol. 290 no. 1 (1985), pp. 259–271
  48. Metrics with holonomy G2 or Spin(7), in Workshop Bonn 1984 (Bonn, 1984), Lecture Notes in Math., edited by F. Hirzebruch, J. Schwermer and S. Suter, vol. 1111 (1985), pp. 269–277, Springer, Berlin--New York
  49. A duality theorem for Willmore surfaces, J. Differential Geom., vol. 20 no. 1 (1984), pp. 23–53
  50. with Phillip A. Griffiths, Some observations on the infinitesimal period relations for regular threefolds with trivial canonical bundle, in Arithmetic and geometry, Vol. II, Progress in Mathematics, edited by Michael Artin and John Tate, vol. 36 (1983), pp. 77–102, Birkhäuser Boston, Boston, MA
  51. with Eric Berger and Phillip Griffiths, The Gauss equations and rigidity of isometric embeddings, Duke Math. J., vol. 50 no. 3 (1983), pp. 803–892
  52. with Phillip Griffiths and Deane Yang, Characteristics and existence of isometric embeddings, Duke Math. J., vol. 50 no. 4 (1983), pp. 893–994
  53. Submanifolds and special structures on the octonians, J. Differential Geom., vol. 17 no. 2 (1982), pp. 185–232
  54. Conformal and minimal immersions of compact surfaces into the 4-sphere, J. Differential Geom., vol. 17 no. 3 (1982), pp. 455-473
  55. Holomorphic curves in Lorentzian CR-manifolds, Trans. Amer. Math. Soc., vol. 272 no. 1 (1982), pp. 203–221
  56. with Shiing-Shen Chern and Phillip Griffiths, Exterior differential systems, in Proceedings of the 1980 Beijing Symposium on Differential Geometry and Differential Equations (Beijing, 1980), edited by S. S. Chern and Wen Tsün Wu, vol. 1 (1982), pp. 219–338, Science Press, Beijing
  57. with Eric Berger and Phillip Griffiths, Some isometric embedding and rigidity results for Riemannian manifolds, Proc. Nat. Acad. Sci. U.S.A., vol. 78 no. 8 (1981), pp. 4657–4660

Papers Submitted

  1. Nonembedding and nonextension results in special holonomy, in Proceedings of the August 2006 Madrid conference in honor of Nigel Hitchin's 60th Birthday, edited by Jean-Pierre Bourguignon, Simon Salamon, and Oscar Garcia Prada (Fall, 2007), Oxford University Press
  2. Gradient Kähler Ricci Solitons, in Proceedings of the conference `Géométrie différentielle, Physique mathématique, Mathématiques et Société' (July 27, 2004)

Papers In Preparation

  1. –––, Calibrated cycles of codimension 3 in compact simple Lie groups , in preparation 1999
  2. –––, A simple definition of $\E_6$ , in preparation 1999

Preprints

  1. with M. Dunajski, M. Eastwood, Metrisability of two-dimensional projective structures (2008)
  2. Real hypersurfaces in unimodular complex surfaces (July 27, 2004)
Last modified: 2008/06/02