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

PhD	University of North Carolina at Chapel Hill	1979
BS	North Carolina State University at Raleigh	1974

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

Duke University: Senior Research Scientist, Mathematics, July 01, 2008 - present

: J. M. Kreps Professor, Mathematics, July 1, 1988 - June 30, 2008

: Arts and Sciences Professor, Mathematics, 1987-88

Mathematical Sciences Research Institute: Director, August 01, 2007 - present

University of California at Berkeley: Professor, Mathematics, July 01, 2007 - present

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

The Geometry of Partial Differential Equations, NSF, Proposal No. 0604195, 2006/07-2007/06.

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: The nearest way: from lines to geometry, Stanford University Department of Mathematics, May 28, 2009; The infinite groupoids of Lie and Cartan, MIT Department of Mathematics, May 23, 2009; Involutive Rational Normal Structures, Chern Institute of Mathematics, Tianjin, China, May 12, 2009; Auf Wiedersehen Surfaces, Revisited, University of Washington, April 03, 2009; On Cartan's generalization of Lie's Third Theorem, Fudan University, Shanghai, China, December 17, 2008; Cartan's Generalization of Lie's Third Theorem, Rutgers University at Newark, November 13, 2008; Riemannian Submersions as PDE, Beijing International Mathematical Research Center, October 27, 2008; Involutive Rational Normal Structures, Institute for Advanced Study, October 17, 2008; Riemannian Submersions as PDE, Harvard Mathematics Department, September 01, 2008; The idea of holonomy, University of Auckland Department of Mathematics, August 07, 2008; Involutive rational normal structures, University of Auckland, August 04, 2008; The geometry of Riemannian submersions and foliations, UC Santa Barbara Mathematics Department, June 06, 2008; Geometric flows and special holonomy, UC Santa Barbara Mathematics Department, June 5, 2008; 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: Abraham D Smith, Integrability of PDE and GL(2,R)-structures on manifolds, (June 1, 2005 - May 10, 2009); Feng Xu, The geometry of SU(3) structures on manifolds, (July 1, 2004 - May 11, 2008); 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

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
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.)
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
Rigidity and quasi-rigidity of extremal cycles in Hermitian symmetric spaces, Annals of Mathematics Studies (to appear)
with S.-S. Chern, Robert B. Gardner, Hubert L. Goldschmidt,and Phillip A. Griffiths, Exterior Differential Systems, MSRI Publications18. Springer-Verlag, New York, 1991
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,
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

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
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
On the geometry of almost complex 6-manifolds, The Asian Journal of Mathematics, vol. 10 no. 3 (September, 2006), pp. 561--606
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
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
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
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
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
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.)
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.)
Some remarks on Finsler manifolds with constant flag curvature, Houston Journal of Mathematics, vol. 28 no. 2 (2002), pp. 221–262
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
Bochner-Kähler metrics, Journal of the AMS, vol. 14 no. 3 (2001), pp. 623–715
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.)
Harmonic morphisms with fibers of dimension one, Communications in Analysis and Geometry, vol. 8 no. 2 (2000), pp. 219–265
Recent advances in the theory of holonomy, Astérisque, vol. 266 no. 5 (2000), pp. 351–374 (Exposé No. 861.)
Élie Cartan and geometric duality, in Journées Élie Cartan 1998 et 1999, vol. 16 (2000), pp. 5–20, Institut Élie Cartan
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).)
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
with Eric Sharpe, D-branes and Spin^c-structures, Phys. Lett. B, vol. 450 no. 4 (1999), pp. 353–357
Some examples of special Lagrangian tori, Adv. Theor. Math. Phys., vol. 3 no. 1 (1999), pp. 83–90
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
Projectively flat Finsler 2-spheres of constant curvature, Selecta Math. (N.S.), vol. 3 no. 2 (1997), pp. 161–203
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
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
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
with Phillip Griffiths, Characteristic cohomology of differential systems, I: General theory, J. Amer. Math. Soc., vol. 8 no. 3 (1995), pp. 507–596
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
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
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
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
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
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
with Lucas Hsu, Rigidity of integral curves of rank 2 distributions, Invent. Math., vol. 114 no. 2 (1993), pp. 435–461
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
Some remarks on the geometry of austere manifolds, Bol. Soc. Brasil. Mat. (N.S.), vol. 21 no. 2 (1991), pp. 133–157
with Simon Salamon, On the construction of some complete metrics with exceptional holonomy, Duke Math. J., vol. 58 no. 3 (1989), pp. 829–850
with F. Reese Harvey, Submanifolds in hyper-Kähler geometry, J. Amer. Math. Soc., vol. 2 no. 1 (1989), pp. 1–31
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
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
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
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
Metrics with exceptional holonomy, Ann. of Math. (2), vol. 126 no. 3 (1987), pp. 525–576
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
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
Lie groups and twistor spaces, Duke Math. J., vol. 52 no. 1 (1985), pp. 223–261
Minimal surfaces of constant curvature in Sⁿ, Trans. Amer. Math. Soc., vol. 290 no. 1 (1985), pp. 259–271
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
A duality theorem for Willmore surfaces, J. Differential Geom., vol. 20 no. 1 (1984), pp. 23–53
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
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
with Phillip Griffiths and Deane Yang, Characteristics and existence of isometric embeddings, Duke Math. J., vol. 50 no. 4 (1983), pp. 893–994
Submanifolds and special structures on the octonians, J. Differential Geom., vol. 17 no. 2 (1982), pp. 185–232
Conformal and minimal immersions of compact surfaces into the 4-sphere, J. Differential Geom., vol. 17 no. 3 (1982), pp. 455-473
Holomorphic curves in Lorentzian CR-manifolds, Trans. Amer. Math. Soc., vol. 272 no. 1 (1982), pp. 203–221
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
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

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
Gradient Kähler Ricci Solitons, in Proceedings of the conference `Géométrie différentielle, Physique mathématique, Mathématiques et Société' (July 27, 2004)

Papers In Preparation

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

Preprints

with M. Dunajski, M. Eastwood, Metrisability of two-dimensional projective structures (2008)
Real hypersurfaces in unimodular complex surfaces (July 27, 2004)

Last modified: 2009/06/12