Curriculum Vitae

Robert Bryant

Box 90320, Durham, NC 27708-0320
(email)
Personal

Born: 1953
Place: Kipling, NC
Citizenship: US

Education

Ph.D.University of North Carolina, Chapel Hill1979
B.S.North Carolina State University1974
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

University of California at Berkeley
Emeritus Professor, Mathematics, August 30, 2013 - present
Professor, Mathematics, July 1, 2007 - June 30, 2013
Duke University
Phillip Griffiths Professor of Mathematics, Mathematics, August 23, 2013 - present
Senior Research Scientist, Mathematics, July 1, 2008 - June 30, 2013
J. M. Kreps Professor, Mathematics, July 1, 1988 - June 30, 2008
Arts and Sciences Professor, Mathematics, 1987-88
Mathematical Sciences Research Institute
Director, August 1, 2007 - July 31, 2013
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

AAAS Fellow, American Association for the Advancement of Science
Distinguished Alumnus, University of North Carolina at Chapel Hill, October 12, 2018
Fellow, American Mathematical Society, 2013
Member, National Academy of Science, 2007
Member, Phi Beta Kappa, 2007
Distinguished Alumni Award from the College of Physical and Mathematical Sciences, NCSU Alumni Association, 2005
American Academy of Arts & Sciences Fellow, 2002
Fellow, American Academy of Arts and Sciences
MAA Southeastern Regional Distinguished Teaching, 1993
Trinity College Distinguished Teaching, 1992
Presidential Young Investigator, 1984
Sloan Research Fellow, 1982
NSF Postdoctoral Research Fellow, 1979
Major Grant Support

DMS-8352009
DMS-8601853
DMS-8905207
DMS-8996110
DMS-9205222
DMS-9505125
DMS-9870164
DMS-0103884
DMS-0604195
DMS-0848131
DMS-1105868

Recent Grant Support

Conferences Organized

Member of Organizing Board, Annual East Coast Geometry Festival, 1 January 1990  
Organizer, Transforming Post-Secondary Education in Mathematics (Duke Regional Meeting), December 05, 2015 - December 06, 2015  
Member, Organizing Committee : Bay Area Differential Geometry Seminar, Member, Organizing Committee : Bay Area Differential Geometry Seminar. 2008 - 2013, 2008 - 2013  
Co-Organizer : Chern Centennial Conference, Co-Organizer : Chern Centennial Conference. October 24, 2011 - November 04, 2011, October 24, 2011 - November 04, 2011  
Conference Organizer, AIM 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
Member, Provost's Advisory Committee on Distinguished Professors, 2015 - present  
Chamber Arts Society of Durham, July 1, 2013 - June 30, 2014  
Faculty Representative, Harassment Grievance Board, July 01, 2005 - June 30, 2008  
Director (since 2000), Chamber Arts Society of Durham, September 1, 1997 - June 30, 2007  
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  
Chair
Chair of the Mathematics Department, Chair of the Mathematics Department. Duke University. July 01, 2021 - June 30, 2024, 2021-24  
Papers Refereed
User and Editor, MathOverflow, 2011 - present  
Moderator, arXiv oversight committee, 2005 - present  
Referee, Refereed for a number of mathematics journals, 1980 - present  
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
Invited Participant, Invited Participant. MPS Workshop on Unity in Numbers: Fostering an Inclusive Community in the Quantitative Sciences. Simons Foundation. May 29, 2024 , 29 May 2024  
Reviewer, Reviewer. Simons Investigators in Mathematics Program. Simons Foundation. 2023 - 2023, 1 January 2023  
Trustee, Trustee. Board of Trustees. The EDGE Foundation. January, 2017, 1 January 2017  
Member, Member. Advisory Board. Project Euclid. 2016, 1 January 2016  
Member, Member. Board of Trustees. Friends of the International Mathematics Union. 2016, 1 January 2016  
Member, Division of Mathematical Sciences Representative, National Science Foundation Math and Physical Science Advisory Committee, July 1, 2014 - present  
Member : Scientific Committee of the IHÉS, Member : Scientific Committee of the IHÉS. June 01, 2013, June 01, 2013 - present  
Chair : Section I:1 (Mathematics and Statistics) panel for 2014 AAAS elections, Chair : Section I:1 (Mathematics and Statistics) panel for 2014 AAAS elections. June 01, 2011, June 01, 2011 - present  
Exterior Member : Academic Council of the Institute Henri Poincaré, Exterior Member : Academic Council of the Institute Henri Poincaré. July 01, 2010, July 01, 2010 - present  
Member of the Board of Directors, Member of the Board of Directors. Friends of the International Mathematics Union. 2009, 1 January 2009  
Member : International Committee for the National Mathematics Centre of Nigeria, Member : International Committee for the National Mathematics Centre of Nigeria. January 01, 2008, January 01, 2008 - present  
Associate Editor, Journal of the American Mathematical Society, February 1, 2005 - present  
Member, Communications in Analysis and Geometry Editorial Board, November 2002 - present  
Member, Duke Mathematical Journal Editorial Board, July 1997 - present  
Member, Member. Mathematical Reviews Editorial Committee. American Mathematical Society. February 01, 2024 - January 31, 2028, 2024-28  
Member (Alternate), Member (Alternate). Board on International Scientific Organizations. National Academies of Science, Engineering, and Medicine. January 01, 2022 - Dece, 2022-26  
Chair, Chair. Conference Board of the Mathematical Sciences. Conference Board of the Mathematical Sciences. December 02, 2023 - December 01, 2026, 2023-26  
Member, Member. 2026 International Congress of Mathematicians Organizing Committee. Simons Foundation. November, 2022 - August, 2026, 2022-26  
Member of Local Organizing Committee, Member of Local Organizing Committee. 2026 International Congress of Mathematicians. International Mathematics Union. August 01, 2022 - August 01, 202, 2022-26  
Member, Member. US National Committee for Mathematics. National Academy of Sciences. January 29, 2019 - June 30, 2026, 2019-26  
Member, Member. Scientific Advisory Board. Berlin Mathematical School. 2018 - 2026, 2018-26  
Invited Attendant, Invited Attendant. MPS Annual Meeting. Simons Foundation. October 17, 2024 - October 18, 2024, October 2024  
Chair, Chair. AAAS-AMS Invited Address Lecture Committee. American Mathematical Society. February 01, 2023 - June 30, 2024, 2023-24  
Member, Member. Advisory Committee for National Center for Theoretical Sciences. NCTS. June 27, 2024 - June 28, 2024, June 2024  
Lead organizer, Lead organizer. Meeting of the Simons Collaboration on Special Holonomy in Geometry, Analysis, and Physics. Duke University. May 13, 2024 - May 17, 20, May 2024  
Lead Organizer, Lead Organizer. Special Holonomy and Geometric Structures on Complex Manifolds. Institute de Mathematica Pura ed Applicada. March 11, 2024 - March 15,, March 2024  
Member, Member. Prize Oversight Committee of the American Mathematical Society. American Mathematical Society. February 01, 2022 - January 31, 2024, 2022-24  
Invited Attendant, Invited Attendant. Mathematics and Physical Sciences Annual Meeting. Simons Foundation. October 12, 2023 - October 13, 2023, October 2023  
Organizer, Organizer. Progress and Open Problems in Special Holonomy. Simons Center for Geometry and Physics. September 10, 2023 - September 13, 2023, September 2023  
Director and Organizer, Director and Organizer. Annual Meeting of the Simons Collaboration on Special Holonomy in Geometry, Analysis, and Physics. Simons Foundation. Septembe, September 2023  
Member, Member. Harvard Mathematics Visiting Committee. Harvard University. March 01, 2023 - March 03, 2023, March 2023  
Member, Member. IAS School of Mathematics Visiting Committee. Institute for Advanced Study. February 01, 2023 - February 03, 2023, February 2023  
Invited Attendant, Invited Attendant. Simons Collaboration on Global Categorical Symmetries Annual Meeting. Simons Foundation. November 17, 2022 - November 18, 2022, November 2022  
Invited Attendant, Invited Attendant. Computational Differential Geometry and its Applications in Physics: November 14-18, 2022. Simons Center for Geometry and Physics. , November 2022  
Invited Attendant, Invited Attendant. Mathematics and Physical Sciences Annual Meeting. Simons Foundation. October 13, 2022 - October 14, 2022, October 2022  
Chair, Chair. Review of Mathematics and Theoretical Computer Science. Institute of Science and Technology, Austria. September 26, 2022 - September 28, 2022, September 2022  
Organizer, Organizer. Progress and Open Problems in Special Holonomy. Simons Center for Geometry and Physics. September 11, 2022 - September 14, 2022, September 2022  
Director and Organizer, Director and Organizer. Annual Meeting of the Simons Collaboration on Special Holonomy. Simons Foundation. September 08, 2022 - September 09, 2022, September 2022  
Member, Member. United States Committee to Secure the 2026 International Congress of Mathematicians. National Academy of Sciences. September, 2021 - August, 2, 2021-22  
Chair, Chair. Committee on Diversity. International Mathematics Union. 2020 - August, 2022, 2020-22  
Invited Attendant, Invited Attendant. Forty Years of Ricci Flow: The Geometric-Flow Revolution in Global Differential Geometry: July 11-15, 2022. Simons Center for Geome, July 2022  
Director, lead Organizer, Director, lead Organizer. Annual Meeting of the Simons Collaboration on Special Holonomy. Simons Foundation. September 09, 2021 - September 10, 2021, September 2021  
Participant, Participant. Faculty Short Course on Improving Departmental Climate. Duke Office of Faculty Advancement & Duke Office of Institutional Equity. August , August 2021  
Section Chair of Section 11 (Mathematics), Section Chair of Section 11 (Mathematics). National Academy of Sciences. May, 2018 - May, 2021, 2018-21  
Member, Member. Mathematics and Physical Sciences Advisory Committee. National Science Foundation. October, 2014 - March, 2021, 2014-21  
Editor, Editor. Communications in Analysis and Geometry. 2003 - 2021, 2003-21  
Member, Member. Search Advisory Committee for the Assistant Director of the MPS Directorate. National Science Foundation. February, 2020 - June, 2020, February-June 2020  
Chair, Chair. Scientific Council. Fondation Mathématique Jacques Hadamard. March, 2016 - March, 2020, 2016-20  
Chair of Membership Committee, Chair of Membership Committee. Class I, Section 1 (Mathematics). American Academy of Arts and Sciences. July, 2012 - June, 2018, 2012-18  
Immediate Past President, Immediate Past President. American Mathematical Society. February, 2017 - February, 2018, 2017-18  
Chair, Chair. Search Committee for new Director of the Division of Mathematical Sciences. National Science Foundation. January, 2017 - June, 2017, January-June 2017  
President of the American Mathematical Society, President of the American Mathematical Society. American Mathematical Society. February 01, 2015 - January 31, 2017, February 01, 2015 - January 31, 2017  
President-elect, Council of the AMS, February 1, 2014 - January 31, 2015  
Member (Class I), National Academy of Sciences Class Membership Committee, November 15, 2013 - November 15, 2014  
Member, Class I Membership Committee, Member, Class I Membership Committee. National Academy of Sciences. November 15, 2013 - November 15, 2014, 2013-14  
Chair : 2014 Chern Medal Committee of the International Mathematical Union, Chair : 2014 Chern Medal Committee of the International Mathematical Union. June 01, 2012 - August 15, 2014, June 01, 2012 - August 15, 2014  
Member : Board of Trustees of the Banff International Research Station, Member : Board of Trustees of the Banff International Research Station. July 01, 2009 - July 31, 2013, July 1, 2009 - July 31, 2013  
Member : StatsNSF, Member : StatsNSF. November 01, 2012 - July, 2013, November 1, 2012 - July 01, 2014  
Deputy Chair, Chair, then Program Chair : Executive Committee of the Golden Section of the MAA, Deputy Chair, Chair, then Program Chair : Executive Committee of the Golden Section of the MAA. March 01, 2008 - February 28, 2011, March 01, 2008 - February 28, 2011  
Member, Differential Geometry and its Applications Editorial Board, May 1, 1999 - August 01, 2010  
Vice President, American Mathematical Society, February 01, 2007 - January 31, 2010  
Director, Park City/IAS Mathematics Institute, January 01, 2007 - August 01, 2009  
Member, AMS Editorial Boards Committee, February 01, 2006 - January 31, 2009  
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  
Univ Services
President's Council on Black Affairs, 2019-22  
Academic Council of Arts and Sciences, 2018-20  
Provost Advisory Committee on Appointments, Promotion, and Tenure, 2016-19  
Advisory Committee on Distinguished Professorships in Arts and Sciences , 2016-18  
Other
Ombud, Ombud. Duke Department of Mathematics. July, 2019, 1 July 2019  
Academic member of the board of directors, The Vietnam Education Foundation, 2002-05  
Selected Recent Invited Talks

Curvature-homogeneous hypersurfaces in space forms, Zoom, 4 December 2024  
Curvature-Homogeneous Hypersurfaces in Space Forms, College Station, TX, 8 November 2024  
Curvature-homogeneous Riemannian manifolds, College Station, TX, 8 November 2024  
Calibrated Geometry and Holonomy, Rice University, 13 September 2024  
The affine Bonnet problem and integrability, Philadelphia, PA, 19 April 2024  
On the Cartan-Kuranishi Prolongation Theorem, New York, NY, 4 May 2022  
On solitons for the closed G2-Laplacian flow, Denver, CO, 17 January 2020  
Curvature-homogeneous metrics in dimension 3., Colorado University-Boulder Mathematics, 2 May 2017  
Engel structures, rigid curves, and compatible complex and symplectic structcures, American Institute of Mathematics, 20 April 2017  
On families of special holonomy metrics defined by algebraic curvature conditions, Simons Center for Geometry and Physics, Stony Brook, NY, September 06, 2016  
Integration techniques for exterior differential systems I & II, Durham, UK, July 27, 2016  
On curvature-homogeneous metrics in dimension 3, Università degli studi Firenze (Florence, Italy), July 11, 2016  
Curvature-homogeneous metrics in dimension 3, Simons Center for Geometry and Physics, Stony Brook, NY, April 28, 2016  
The geometry and dynamics of uniformly periodic recursion relations, Vanderbilt University, April 21, 2016  
The geometry and dynamics of periodic equi-areal sequences, Tulane University Mathematics Department, February 25, 2016  
Beyond Holonomy: Constrained Structure Equations, Institut Henri Poincaré, Paris, France, December 14, 2015  
Curvature-homogeneous metrics in dimension 3, Howard University, Washington, DC, October 24, 2015  
On curvature-homogeneous 3-manifolds, Howard University, 24 October 2015  
On curvature-homogeneous 3-manifolds, University College Cork, Cork, Ireland, October 13, 2015  
The idea of holonomy, University College Cork, Cork, Ireland, October 12, 2015  
The geometry of periodic equi-Poisson sequences, University of California, Irvine, Mathematics Department, May 29, 2015  
The geometry of equi-areal sequences, North Carolina State University Mathematics Department, January 29, 2015  
G-structures with prescribed geometry, The 35th Winter School in GEOMETRY AND PHYSICS, Srní, Czech Republic, January 18-20, 2015  
Some geometric constructions of holonomy plane fields and their analysis, Institut Henri Poincaré, Paris France, December 10, 2014  
Some exceptional geometry of rolling surfaces, UNC Greensboro, November 09, 2014  
Convex billiards and non-holonomic systems, University of Colorado at Boulder , October 14, 2014  
The idea of holonomy, University of Colorado at Boulder, October 13, 2014  
Riemannian manifolds with special holonomy and special curvature, Simons Center for Geometry and Physics, Stony Brook, NY, September 30, 2014  
On G_2 and complex and almost-complex structures on 6-manifolds, London, UK, 14 July 2014  
On G_2 and complex and almost-complex structures on 6-manifolds, University College London, July 14, 2014  
The Geometry of Special Holonomy Metrics, Imperial College, London, UK, July 7-11, 2014  
The geometry of periodic equi-areal sequences, Banach Center, Warsaw, Poland, June 05, 2014  
Existence and Non-Existence of Canonical Connections, Banach Center, Warsaw, Poland, June 03, 2014  
Differential Systems and Holonomy, UCLA Mathematics Distinguished Lecture Series, May, 2014  
Rolling surfaces and exceptional geometry, Stony Brook University (29th Geometry Festival), April 11, 2014  
The geometry of rolling surfaces and non-holonomic mechanics, UT-Knoxville, Smoky Cascade Geometry Conference, March 21, 2014  
Exterior Differential Systems and Lie Theory, IV: Examples and Applications, Fields Institute, Toronto, CA, December 12, 2013  
Exterior Differential Systems and Lie Theory, II: The basics of Cartan-Kähler Theory, Fields Institute, Toronto, CA, December 11, 2013  
Exterior Differential Systems and Lie Theory, III: The structure theory and existence, Fields Institute, Toronto, CA, December 10, 2013  
Exterior Differential Systems and Lie Theory, I: Introduction, Fields Institute, Toronto, CA, December 9, 2013  
Prescribed curvature in Finsler geometry and PDE, Beijing Institute of Technology, November 20, 2013  
Riemann-Finsler geometry and the Method of Equivalence, Beijing International Center for Mathematical Research, November 15, 2013  
The geometry of equi-Poisson sequences, University of Melbourne, Melbourne, AU, November 08, 2013  
Recent developments in special holonomy manifolds, University of Adelaide, Dept. of Mathematics, November 01, 2013  
The geometry of rolling surfaces and non-holonomic mechanics, University of Adelaide, Dept. of Mathematics, November 01, 2013  
Finsler manifolds of constant flag curvature, University of Adelaide, Dept. of Mathematics, October 31, 2013  
The origins of Finsler geometry in the calculus of variations, University of Adelaide, Dept. of Mathematics, October 31, 2013  
The geometry of calibrations, Australian National University Mathematics Department, Canberra, AU, October 24, 2013  
Convex Billiards and nonholonomic systems, University of Sydney, Sydney, AU, October 09, 2013  
Recent advances in the geometry of PDE, Australian Mathematical Society Annual Meeting, Sydney, AU, October 03, 2013  
The Affine Bonnet Problem, Australian Mathematical Society Annual Meeting, Sydney, AU, October 1, 2013  
On the geometry of rolling surfaces, Institute Élie Cartan, Nancy, September 17, 2013  
A visit to the Finsler world, Institute des Hautes Études Scientifiques, September 13, 2013  
Introduction to Holonomy, II, CUNY Graduate School, New York, NY, May 29, 2013  
Introduction to Holonomy, I, CUNY Graduate School, New York, NY, May 28, 2013  
Parking Cars, Rolling Balls, and Falling Cats: The Concept of Holonomy, Simons Foundation in New York City, May 22, 2013  
Convex billiards and nonholonomic systems, Humboldt State University, Arcata, CA, November 01, 2012  
Geometry Old and New: From Euclid to String Theory, Humboldt State University, Arcata, CA, November 1, 2012  
On the local classification of ambiKähler structures in dimension 4, SUNY Stony Brook, October 27, 2012  
Geometry Old and New: From Euclid to String Theory, SUMS conference, James Madison University, September 29, 2012  
On normal forms for Pfaffian systems and their application, Erwin Schrödinger Institute, Vienna, September 12, 2012  
Some geometry of characteristic cohomology, Hausdorf Institute of Mathematics, Bonn, DE, January 23, 2012  
Applications of Cartan's generalization of Lie's Third Theorem, Centre de Rescherches Mathématiques, Montreal, CA, June 13, 2011  
On the affine Bonnet problem, IMPA, Rio de Janeiro, Brazil, May 17, 2011  
On the affine Bonnet problem, RIMS, Kyoto Japan, January 24, 2011  
The Affine Bonnet Problem, Center for Mathematical Sciences, Technion Institute, Israel, December 16, 2010  
Cartan's Generalization of Lie's Third Fundamental Theorem, Center for Mathematical Sciences, Technion Institute, Israel, December 15, 2010  
A visit to the Finsler world, Center for Mathematical Sciences, Technion Institute, Israel, December 13, 2010  
The Affine Bonnet Problem, Texas A&M Department of Mathematics, November 14, 2010  
The Affine Bonnet Problem, Notre Dame University, October 22, 2010  
The Affine Bonnet Problem, Pacific Northwest Geometry Seminar, Eugene, OR, October 17, 2010  
The idea of Holonomy, MAA Carriage House, Washington, DC, October 14, 2010  
On the life and work of S.-S. Chern, ICM in Hyderabad, India, August 19, 2010  
A visit to the Finsler world, Joint meeting of the AMS and the Mexican Mathematical Society, June 02, 2010  
On the geometry of projective surfaces, Universidade da Brasília, May 25, 2010  
Auf Wiedersehen Surfaces, Revisited, Northwestern University Mathematics, March 10, 2010  
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

Michael Bell, Second-Order Families of Minimal Lagrangians in CP^3, (2015 - September, 2019)  
Gavin Ball, Seven-Dimensional Geometries With Special Torsion, (2015 - May, 2019)  
Ryan Gunderson, Riemannian 3-Manifolds with a Flatness Condition, (2015 - May, 2019)  
Yuhao Y. Hu, Geometry of Bäcklund Transformations, (2015 - May, 2018)  
Zhiyong Zhao, Complex and Lagrangian Engel Structures, (2015 - May, 2018)  
Jesse O. Madnick, Cohomogeneity Two Nearly-Kähler structures, (2012 - May, 2018)  
Benjamin McMillan, Geometry and Conservtion Laws for a Class of Second Order Parabolic Equations, (July, 2012 - May, 2016)  
Conrad A. Hengesbach, Prescribed Mean Curvature Systems, (2006 - December, 2012)  
Abraham D Smith, Integrability of PDE and GL(2,R)-structures on manifolds, (2009)  
Feng Xu, The geometry of SU(3) structures on manifolds, (2008)  
Dan Fox, Second order families of coassociative submanifolds, (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
Association for Women in Mathematics
National Association of Mathematicians
National Academy of Sciences
American Academy of Arts and Sciences
Chamber Arts Society of Durham (Director emeritus)

Publications

Books

  1. with Bryant, RL; Chern, SS; Gardner, RB; Goldschmidt, HL; Griffiths, PA, Exterior Differential Systems (December, 2011), pp. 475 pages, Springer, ISBN 9781461397168
  2. with Gu, C; Berger, M; Bryant, RL, Differential Geometry and Differential Equations Proceedings of a Symposium, held in Shanghai, June 21 - July 6, 1985 (November, 2006), pp. 246 pages, Springer, ISBN 9783540478836
  3. with Bao, DD-W, A Sampler of Riemann-Finsler Geometry, Mathematical Sciences Research Institute Publications, edited by Bao, D; Bryant, RL; Chern, S-S; Shen, Z, vol. 50 (November, 2004), pp. 363 pages, Cambridge University Press, ISBN 9780521831819
  4. with Bryant, R; Griffiths, P; Grossman, D, Exterior Differential Systems and Euler-Lagrange Partial Differential Equations, Chicago Lectures in Mathematics (July, 2003), pp. 213 pages, University of Chicago Press, ISBN 9780226077932 (vii+213 pages, ISBN: 0-226-07794-2.)
  5. 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
  6. with Victor Guillemin, Sigurdur Helgason, and R. O. Wells, Jr. (eds.), Integral Geometry, edited by Bryant, R; Guillemin, V; Helgason, S; Wells, RO, vol. 63 (1987), pp. 350 pages, American Mathematical Society, ISBN 0-8218-5071-7
  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. Buckmire, R; Beeton, B; Bryant, R; Gouvêa, FQ; Phillips, AV; Sullivan, D; Wolf, M, Michael Spivak: A Memorial, Notices of the American Mathematical Society, vol. 71 no. 6 (June, 2024), pp. 786-795
  2. Bryant, R; Cheeger, J; Lima-Filho, P; Rosenberg, J; White, B, The mathematical work of H. Blaine Lawson, Jr., Pure and Applied Mathematics Quarterly, vol. 19 no. 6 (January, 2024), pp. 2627-2662, International Press
  3. Bryant, R, The generality of closed G_2 solitons, edited by Cheng, S-Y; Lima-Filho, P; Yau, SS-T; Yau, S-T, Pure and Applied Mathematics Quarterly, vol. 19 no. 6 (January, 2024), pp. 2827-2840, International Press
  4. Bryant, R; Cheeger, J; Griffiths, P; Blum, L; Burns, D; Connes, A; Donnelly, H; Ebin, D; Guillemin, V; Palais, R; Rossi, H; Simons, J; Singer, E; Singer, N; Stanton, N; Sternberg, S, Isadore M. Singer (1924–2021) In Memoriam Part 2: Personal Recollections, Notices of the American Mathematical Society, vol. 69 no. 10 (November, 2022), pp. 1-1, American Mathematical Society (AMS)
  5. Bryant, R; Bismut, J-M; Cheeger, J; Griffiths, P; Donaldson, S; Hitchin, N; Lawson, HB; Gromov, M; Marcus, A; Spielman, D; Srivastava, N; Witten, E, Isadore M. Singer (1924–2021) In Memoriam Part 1: Scientific Works, Notices of the American Mathematical Society, vol. 69 no. 09 (October, 2022), pp. 1-1, American Mathematical Society (AMS)
  6. Phong, DH; Siu, Y-T; Bryant, R; Chau, A; Falbel, E; Fefferman, C; Friedman, R; Morgan, J; Futaki, A; Griffiths, P; Kohn, JJ; Mok, N; Mori, S; Namba, M; Noguchi, J; Ohsawa, T; Sato, M; Yau, S-T, Masatake Kuranishi (1924–2021), Notices of the American Mathematical Society, vol. 69 no. 05 (May, 2022), pp. 1-1, American Mathematical Society (AMS)
  7. Bryant, RL, S.-S. Chern’s study of almost-complex structures on the six-sphere, edited by Bryant, R; Cheng, SY; Griffiths, P; Ma, X; Ni, L; Wallach, N, International Journal of Mathematics, vol. 32 no. 12 (November, 2021), World Scientific Publishing
  8. Bryant, RL; Foulon, P; Ivanov, SV; Matveev, VS; Ziller, W, Geodesic behavior for Finsler metrics of constant positive flag curvature on S2, Journal of Differential Geometry, vol. 117 no. 1 (January, 2021), pp. 1-22
  9. Acharya, BS; Bryant, RL; Salamon, S, A circle quotient of a G2 cone, Differential Geometry and its Application, vol. 73 (December, 2020), pp. 43 pages, Elsevier
  10. Bryant, RL, Notes on spinors in low dimension (November, 2020)
  11. Bryant, RL; Clelland, JN, Flat metrics with a prescribed derived coframing, Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), vol. 16 (January, 2020), National Academy of Science of Ukraine
  12. Bryant, RL; Eastwood, MG; Gover, AR; Neusser, K, Some differential complexes within and beyond parabolic geometry, Advanced Studies in Pure Mathematics, vol. 82 no. Differential Geometry and Tanaka Theory (November, 2019), pp. 13-40, Mathematical Society of Japan
  13. Bryant, R; Buckmire, R; Khadjavi, L; Lind, D, The origins of spectra, an organization for LGBT mathematicians, Notices of the American Mathematical Society, vol. 66 no. 6 (June, 2019), pp. 875-882
  14. Bryant, RL, Notes on Projective, Contact, and Null Curves (May, 2019)
  15. Bryant, RL; Huang, L; Mo, X, On Finsler surfaces of constant flag curvature with a Killing field, Journal of Geometry and Physics, vol. 116 (June, 2017), pp. 345-357, Elsevier BV
  16. Bryant, RL, On the Convex Pfaff-Darboux Theorem of Ekeland and Nirenberg, SIGMA 19, vol. 060 (December, 2015), pp. 10
  17. Bryant, RL, On the conformal volume of 2-tori (July, 2015)
  18. Bryant, RL, Notes on exterior differential systems (May, 2014)
  19. Bryant, RL, Complex analysis and a class of Weingarten surfaces (May, 2011), pp. 10 pages
  20. Bryant, R; Xu, F, Laplacian Flow for Closed $G_2$-Structures: Short Time Behavior (January, 2011)
  21. Bryant, RL, Non‐Embedding and Non‐Extension Results in Special Holonomy, in The Many Facets of Geometry, edited by Garcia-Prada, O; Bourguignon, JP; Salamon, S (Fall, 2010), pp. 346-367, Oxford University Press, Oxford, ISBN 0199534926
  22. Bryant, RL, Commentary, Bulletin of the American Mathematical Society, vol. 46 no. 2 (April, 2009), pp. 177-178, American Mathematical Society (AMS), ISSN 0273-0979
  23. with Bryant, R; Dunajski, M; Eastwood, M, Metrisability of two-dimensional projective structures, Journal of Differential Geometry, vol. 83 no. 3 (January, 2009), pp. 465-500, International Press of Boston, ISSN 0022-040X
  24. Bryant, RL, GRADIENT KAHLER RICCI SOLITONS, in Géométrie différentielle, physique mathématique, mathématiques et société. I., Astérisque, ASTERISQUE, vol. 321 no. 321 (Spring, 2008), pp. 51-97, SOC MATHEMATIQUE FRANCE, ISBN 978-285629-258-7
  25. with Bryant, RL; Manno, G; Matveev, VS, A solution of a problem of Sophus Lie: Normal forms of two-dimensional metrics admitting two projective vector fields, Mathematische Annalen, vol. 340 no. 2 (Spring, 2008), pp. 437-463, Springer Nature America, Inc
  26. Bryant, RL, GEODESICALLY REVERSIBLE FINSLER 2-SPHERES OF CONSTANT CURVATURE, in Nankai Tracts in Mathematics, Nankai Tracts in Mathematics, edited by Griffiths, PA, vol. 11 (Winter, 2006), pp. 95-111, WORLD SCIENTIFIC, ISBN 9789812700612
  27. Bryant, RL, On the geometry of almost complex 6-manifolds, ASIAN JOURNAL OF MATHEMATICS, vol. 10 no. 3 (September, 2006), pp. 561-605, INT PRESS
  28. Bryant, RL, CONFORMAL GEOMETRY AND 3-PLANE FIELDS ON 6-MANIFOLDS(Developments of Cartan Geometry and Related Mathematical Problems), in Developments of Cartan Geometry and Related Mathematical Problems, RIMS Symposium Proceedings, 数理解析研究所講究録, vol. 1502 (July, 2006), pp. 1-15, 京都大学
  29. Bryant, R; Freed, D, Shiing-Shen Chern, Physics Today, vol. 59 no. 1 (January, 2006), pp. 70-72, AIP Publishing
  30. Bryant, RL, Geometry of manifolds with special holonomy: "100 years of holonomy", in 150 years of mathematics at Washington University in St. Louis, Contemporary Mathematics, edited by Jensen, GR; Krantz, SG, 150 Years of Mathematics at Washington University in St. Louis, vol. 395 (January, 2006), pp. 29-38, AMER MATHEMATICAL SOC, ISBN 0-8218-3603-X
  31. Bryant, RL, SO(n)-Invariant special lagrangian submanifolds of Cn+1 with fixed loci, CHINESE ANNALS OF MATHEMATICS SERIES B, vol. 27 no. 1 (January, 2006), pp. 95-112, SHANGHAI SCIENTIFIC TECHNOLOGY LITERATURE PUBLISHING HOUSE
  32. Bryant, RL, Second order families of special Lagrangian 3-folds, in Perspectives in Riemannian Geometry, CRM Proceedings and Lecture Notes, edited by Apostolov, V; Dancer, A; Hitchin, N; Wang, M, Perspectives in Riemannian Geometry, vol. 40 (January, 2006), pp. 63-98, AMER MATHEMATICAL SOC, ISBN 0-8218-3852-0
  33. Bryant, R, Holonomy and Special Geometries, in Dirac Operators: Yesterday and Today, Conference Proceedings and Lecture Notes in Geometry and Topology, edited by Bourguinon, JP; Branson, T; Chamseddine, A; Hijazi, O; Stanton, R (2005), pp. 71-90, International Press, ISBN 1-57146-175-2 (Proceedings of the Summer School and Workshop at CAMS-AUB, Lebanon, August 27 -- September 7, 2001.)
  34. Bryant, RL, Real hypersurfaces in unimodular complex surfaces (July, 2004)
  35. with Bryant, R; Edelsbrunner, H; Koehl, P; Levitt, M, The area derivative of a space-filling diagram, Discrete and Computational Geometry, vol. 32 no. 3 (January, 2004), pp. 293-308, Springer Nature (ISSN: 0179-5376.)
  36. Bryant, RL, Some remarks on G_2-structures, in Proceedings of Gökova Geometry-Topology Conference 2005, edited by Akbulut, S; Onder, T; Stern, R (May, 2003), pp. 75-109, International Press, ISBN 1-57146-152-3
  37. Bryant, RL, Some remarks on Finsler manifolds with constant flag curvature, HOUSTON JOURNAL OF MATHEMATICS, vol. 28 no. 2 (January, 2002), pp. 221-262, UNIV HOUSTON
  38. 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
  39. Bryant, RI, On Surfaces with Prescribed Shape Operator, Results in Mathematics, vol. 40 no. 1-4 (October, 2001), pp. 88-121, Springer Science and Business Media LLC (Dedicated to Shiing-Shen Chern on his 90th birthday.)
  40. Bryant, RL, Bochner-Kahler metrics, JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY, vol. 14 no. 3 (January, 2001), pp. 623-715, AMER MATHEMATICAL SOC
  41. Bryant, RL, Calibrated embeddings in the special Lagrangian and coassociative cases, ANNALS OF GLOBAL ANALYSIS AND GEOMETRY, vol. 18 no. 3-4 (August, 2000), pp. 405-435, SPRINGER (Special issue in memory of Alfred Gray (1939--1998).)
  42. Bryant, RL, Rigidity and quasi-rigidity of extremal cycles in Hermitian symmetric spaces (June, 2000)
  43. Bryant, RL, Pseudo-Riemannian metrics with parallel spinor fields and vanishing Ricci tensor, in Global analysis and harmonic analysis (Marseille-Luminy, 1999), Séminaires & Congrès, edited by Bourguinon, JP; Branson, T; Hijazi, O, vol. 4 (April, 2000), pp. 53-94, Société Mathématique de France, ISBN 2-85629-094-9
  44. Bryant, RL, Harmonic morphisms with fibers of dimension one, COMMUNICATIONS IN ANALYSIS AND GEOMETRY, vol. 8 no. 2 (April, 2000), pp. 219-265, INT PRESS CO LTD
  45. Bryant, R, Recent advances in the theory of holonomy, ASTERISQUE, vol. 266 no. 266 (January, 2000), pp. 351-+, SOC MATHEMATIQUE FRANCE (Exposé No. 861.)
  46. Bryant, R, Élie Cartan and geometric duality, in Journées Élie Cartan 1998 et 1999, Journées Élie Cartan 1998 et 1999, vol. 16 (2000), pp. 5-20, Institut Élie Cartan
  47. Bryant, RL, Recent Advances in the Theory of Holonomy, Seminaire Bourbaki, vol. 1998 no. 99 (October, 1999), pp. 351-374
  48. Bryant, RL, Levi-flat Minimal Hypersurfaces in Two-dimensional Complex Space Forms, Adv. Stud. Pure Math., 37, Math. Soc. Japan, Tokyo, 2002, 1--44 (September, 1999)
  49. Bryant, RL, Some examples of special Lagrangian tori, Advances in Theoretical and Mathematical Physics, vol. 3 no. 1 (1999), pp. 83-90, International Press of Boston
  50. with Sharpe, E; Bryant, RL, D-branes and Spin^c-structures, Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics, vol. 450 no. 4 (1999), pp. 353-357, Elsevier BV
  51. 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
  52. Bryant, RL, Projectively flat Finsler 2-spheres of constant curvature, Selecta Mathematica, vol. 3 no. 2 (June, 1997), pp. 161-203, Springer Science and Business Media LLC
  53. 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
  54. Bryant, R, Classical, exceptional, and exotic holonomies: a status report, in Actes de la Table Ronde de Géométrie Différentielle, Sémin. Congr., edited by Besse, A, vol. 1 (1996), pp. 93-165, Société Mathématique de France, ISBN 2-85629-047-7
  55. with Bryant, R; Griffiths, P; Hsu, L, Hyperbolic exterior differential systems and their conservation laws, part II, Selecta Mathematica, New Series, vol. 1 no. 2 (September, 1995), pp. 265-323, Springer Nature
  56. Bryant, RL; Griffiths, PA, Characteristic Cohomology of Differential Systems (I): General Theory, Journal of the American Mathematical Society, vol. 8 no. 3 (July, 1995), pp. 507-507, JSTOR
  57. BRYANT, RL; GRIFFITHS, PA, CHARACTERISTIC COHOMOLOGY OF DIFFERENTIAL-SYSTEMS .1. GENERAL-THEORY, JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY, vol. 8 no. 3 (July, 1995), pp. 507-596, AMER MATHEMATICAL SOC
  58. with BRYANT, RL; GRIFFITHS, PA, CHARACTERISTIC COHOMOLOGY OF DIFFERENTIAL-SYSTEMS .2. CONSERVATION-LAWS FOR A CLASS OF PARABOLIC EQUATIONS, DUKE MATHEMATICAL JOURNAL, vol. 78 no. 3 (June, 1995), pp. 531-676, DUKE UNIV PRESS
  59. with Bryant, R; Griffiths, P; Hsu, L, Hyperbolic exterior differential systems and their conservation laws, part I, Selecta Mathematica, New Series, vol. 1 no. 1 (March, 1995), pp. 21-112, Springer Nature
  60. with BRYANT, R; GRIFFITHS, P; HSU, L, TOWARD A GEOMETRY OF DIFFERENTIAL-EQUATIONS, in Geometry, Topology, & Physics, Conf. Proc. Lecture Notes Geom. Topology, edited by Yau, ST, GEOMETRY, TOPOLOGY & PHYSICS, vol. 4 (January, 1995), pp. 1-76, INTERNATIONAL PRESS INC BOSTON, ISBN 1-57146-024-1
  61. with Bryant, R; Gardner, RB, Control Structures, in Geometry in nonlinear control and differential inclusions (Warsaw, 1993), Banach Center Publications, edited by Jakubczyk, B; Respondek, W; Rzezuchowski, T, vol. 12 (1995), pp. 111-121, Polish Academy of Sciences
  62. Bryant, R, An introduction to Lie groups and symplectic geometry, in Geometry and quantum field theory (Park City, UT, 1991), IAS/Park City Mathematics, edited by Freed, D; Uhlenbeck, K, vol. 1 (1995), pp. 5-181, American Mathematical Society, ISBN 0-8218-0400-6
  63. Bryant, RL, On extremals with prescribed Lagrangian densities, in Manifolds and geometry (Pisa, 1993), Symposia Mathematica, edited by Bartolomeis, P; Tricerri, F; Vesentini, E, vol. 36 (June, 1994), pp. 86-111, Cambridge University Press, ISBN 0-521-56216-3
  64. with Bryant, RL; Hsu, L, Rigidity of integral curves of rank 2 distributions, Inventiones Mathematicae, vol. 114 no. 1 (December, 1993), pp. 435-461, Springer Nature, ISSN 0020-9910
  65. Bryant, RL, Some remarks on the geometry of austere manifolds, Boletim da Sociedade Brasileira de Matemática, vol. 21 no. 2 (September, 1991), pp. 133-157, Springer Nature
  66. Bryant, R, 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 Carlson, J; Clemens, H; Morrison, D, vol. 53 (1991), pp. 33-88, American Mathematical Society, ISBN 0-8218-1492-3
  67. with Bryant, R; Harvey, R, Submanifolds in hyper-Kähler geometry, Journal of the American Mathematical Society, vol. 2 no. 1 (January, 1989), pp. 1-31, American Mathematical Society (AMS)
  68. with Bryant, RL; Salamon, SM, On the construction of some complete metrics with exceptional holonomy, Duke Mathematical Journal, vol. 58 no. 3 (January, 1989), pp. 829-850, Duke University Press
  69. Bryant, R, Surfaces in conformal geometry, in The mathematical heritage of Hermann Weyl (Durham, NC, 1987), Proc. Sympos. Pure Math., edited by Wells, RO, vol. 48 (1988), pp. 227-240, American Mathematical Society, ISBN 0-8218-1482-6
  70. Bryant, R, Surfaces of mean curvature one in hyperbolic space, in Théorie des variétés minimales et applications (Palaiseau, 1983–1984), Astérisque, vol. 154-155 (1988), pp. 321-347, Société Mathématique de France
  71. Bryant, RL, Metrics with Exceptional Holonomy, The Annals of Mathematics, vol. 126 no. 3 (November, 1987), pp. 525-525, JSTOR
  72. Bryant, R, 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 Luksic, M; Martin, C; Shadwick, W, vol. 68 (1987), pp. 65-76, American Mathematical Society, ISBN 0-8218-5075-X
  73. Bryant, R, A survey of Riemannian metrics with special holonomy groups, in Proceedings of the International Congress of Mathematicians. Vol. 1, 2. (Berkeley, Calif., 1986), edited by Gleason, A (1987), pp. 505-514, American Mathematical Society, ISBN 0-8218-0110-4
  74. Bryant, R, Minimal Lagrangian submanifolds of Kähler-Einstein manifolds, in Differential geometry and differential equations (Shanghai, 1985), Lecture Notes in Math., edited by Gu, C; Berger, M; Bryant, RL, vol. 1255 (1987), pp. 1-12, Springer-Verlag, ISBN 3-540-17849-X
  75. with BRYANT, R; GRIFFITHS, P, REDUCTION FOR CONSTRAINED VARIATIONAL-PROBLEMS AND INTEGRAL-K2/2DS, AMERICAN JOURNAL OF MATHEMATICS, vol. 108 no. 3 (June, 1986), pp. 525-570, JOHNS HOPKINS UNIV PRESS
  76. Bryant, RL, Minimal surfaces of constant curvature in sn, Transactions of the American Mathematical Society, vol. 290 no. 1 (January, 1985), pp. 259-271, JSTOR
  77. Bryant, RL, Lie groups and twlstor spaces, Duke Mathematical Journal, vol. 52 no. 1 (January, 1985), pp. 223-261, Duke University Press
  78. Bryant, R, Metrics with holonomy G2 or Spin(7), in Workshop Bonn 1984 (Bonn, 1984), Lecture Notes in Math., edited by Hirzebruch, F; Schwermer, J; Suter, S, vol. 1111 (1985), pp. 269-277, Springer
  79. Bryant, RL, A duality theorem for willmore surfaces, Journal of Differential Geometry, vol. 20 no. 1 (January, 1984), pp. 23-53, International Press of Boston
  80. with Berger, E; Bryant, R; Griffiths, P, The Gauss equations and rigidity of isometric embeddings, Duke Mathematical Journal, vol. 50 no. 3 (January, 1983), pp. 803-892, Duke University Press
  81. with Bryant, RL; Griffiths, PA; Yang, D, Characteristics and existence of isometric embeddings, Duke Mathematical Journal, vol. 50 no. 4 (January, 1983), pp. 893-994, Duke University Press
  82. with Bryant, R; Griffiths, PA, 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 Artin, M; Tate, J, vol. 36 (1983), pp. 77-102, Birkhäuser Boston, ISBN 3-7643-3133-X
  83. Bryant, RL, Holomorphic curves in lorentzian cr-manifolds, Transactions of the American Mathematical Society, vol. 272 no. 1 (January, 1982), pp. 203-221, American Mathematical Society (AMS)
  84. Bryant, RL, Submanifolds and special structures on the octonians, Journal of Differential Geometry, vol. 17 no. 2 (January, 1982), pp. 185-232, International Press of Boston
  85. Bryant, RL, Conformal and minimal immersions of compact surfaces into the 4-sphere, Journal of Differential Geometry, vol. 17 no. 3 (January, 1982), pp. 455-473, International Press of Boston
  86. with Bryant, R; Chern, SS; Griffiths, PA, Exterior Differential Systems, in Proceedings of the 1980 Beijing Symposium on Differential Geometry and Differential Equations (Beijing, 1980), edited by Chern, SS; Wu, WT, vol. 1 (1982), pp. 219-338, Science Press; Gordon & Breach Science Publishers, ISBN 0-677-16420-3
  87. with BERGER, E; BRYANT, R; GRIFFITHS, P, SOME ISOMETRIC EMBEDDING AND RIGIDITY RESULTS FOR RIEMANNIAN-MANIFOLDS, PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA-PHYSICAL SCIENCES, vol. 78 no. 8 (1981), pp. 4657-4660

Papers Accepted

  1. with Michael G. Eastwood, A. Rod. Gover, Katharina Neusser, Some differential complexes within and beyond parabolic geometry (December, 2011)

Papers In Preparation

  1. R. Bryant, On the geometry of curvature-homogeneous Riemannian 3-manifolds (2015)
  2. R. Bryant, On the affine Bonnet problem for surfaces (2015)
  3. R.L. Bryant, Equi-Poisson sequences (2013)
  4. R.L. Bryant, Hessianizability of Cubic Forms in Dimensions 2 and 3 (2013)
  5. –––, Calibrated cycles of codimension 3 in compact simple Lie groups , in preparation 1999
  6. –––, A simple definition of $\E_6$ , in preparation 1999

Preprints

  1. Bryant, RL, Hessianizability of surface metrics (May, 2024)
  2. Bryant, R; Florit, L; Ziller, W, Curvature homogeneous hypersurfaces in space forms (April, 2024)
  3. R.L. Bryant and Feng Xu, Laplacian flow for closed G2-structures: short time behavior (January, 2011)
Last modified: 2025/02/21