Robert Bryant
Phillip Griffiths Professor of Mathematics
My research concerns problems in the geometric theory of partial differential equations. More specifically, I work on conservation laws for PDE, Finsler geometry, projective geometry, and Riemannian geometry, including calibrations and the theory of holonomy.
Much of my work involves or develops techniques for studying systems of partial differential equations that arise in geometric problems. Because of their built-in invariance properties, these systems often have special features that make them difficult to treat by the standard tools of analysis, and so my approach uses ideas and techniques from the theory of exterior differential systems, a collection of tools for analyzing such PDE systems that treats them in a coordinate-free way, focusing instead on their properties that are invariant under diffeomorphism or other transformations.
I’m particularly interested in geometric structures constrained by natural conditions, such as Riemannian manifolds whose curvature tensor satisfies some identity or that supports some additional geometric structure, such as a parallel differential form or other geometric structures that satisfy some partial integrability conditions and in constructing examples of such geometric structures, such as Finsler metrics with constant flag curvature.I am also the Director of the Simons Collaboration Special Holonomy in Geometry, Analysis, and Physics, and a considerable focus of my research and that of my students is directed towards problems in this area.
Current Research Interests
Exterior differential systems, Finsler geometry, differential geometry, geometry of partial differential equations
Office Hours
Tuesdays and Thursdays, 10:30-12:00PM, and by appointment (currently, all office hours are virtual)
Current Appointments & Affiliations
- Phillip Griffiths Professor of Mathematics, Mathematics, Trinity College of Arts & Sciences 2013
- Professor in the Department of Mathematics, Mathematics, Trinity College of Arts & Sciences 1987
Contact Information
- 103 Physics Bldg, West Campus, Durham, NC 27708
- Box 90320, Durham, NC 27708-0320
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bryant@math.duke.edu
(919) 660-2817
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#Personal Website
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Interview with Notices of AMS
- Background
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Education, Training, & Certifications
- Ph.D., University of North Carolina - Chapel Hill 1979
- B.S., North Carolina State University 1974
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Duke Appointment History
- Professor in the Department of Computer Science, Computer Science, Trinity College of Arts & Sciences 2014 - 2016
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Leadership & Clinical Positions at Duke
- Ombudsperson, July 2019
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Academic Positions Outside Duke
- Emeritus Professor of Mathematics, University of California at Berkeley. 2013 - 2053
- Director, Mathematical Sciences Research Institute. 2007 - 2013
- Professor of Mathematics, University of California at Berkeley. 2007 - 2013
- Noah Harding Professor of Mathematics, Rice University. 1986 - 1988
- Professor of Mathematics, Rice University. 1982 - 1986
- Recognition
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In the News
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JUN 1, 2019 The Notices of the American Mathematical Society -
OCT 1, 2018 The Notices of the American Mathematical Society -
JUN 1, 2016 Notices of the AMS -
MAR 1, 2015 The Notices of the American Mathematical Society -
DEC 10, 2013
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Awards & Honors
- Expertise
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Subject Headings
- Research
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Selected Grants
- Special Holonomy In Geometry, Analysis and Physics awarded by Simons Foundation 2020 - 2023
- Special Holonomy In Geometry, Analysis and Physics awarded by Simons Foundation 2016 - 2020
- The Geometry of Partial Differential Equations and Applications awarded by National Science Foundation 2013 - 2015
- The Geometry of Partial Differential Equations awarded by National Science Foundation 2006 - 2008
- The Differential Geometry of Partial Differential Equations awarded by National Science Foundation 2001 - 2006
- The Differential Geometry of Partial Differential Equations awarded by National Science Foundation 1998 - 2001
- Mathematical Sciences: The Differential Geometry of Partial Differential Equations awarded by National Science Foundation 1995 - 1998
- Mathematical Sciences: The Differential Geometry of Partial Differential Equations awarded by National Science Foundation 1995 - 1997
- The Differential Geometry of Partial Differential Equations awarded by National Science Foundation 1995 - 1997
- The Differential Geometry of Partial Differential Equations awarded by National Science Foundation 1992 - 1995
- Mathematical Sciences: Differential Geometry awarded by National Science Foundation 1989 - 1993
- Differential Geometry awarded by National Science Foundation 1989 - 1990
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External Relationships
- Institut des Hautes Etudes Scientifiques
- MathX
- Simons Foundation
- Publications & Artistic Works
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Selected Publications
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Books
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Bryant, Robert L., S. S. Chern, Robert B. Gardner, Hubert L. Goldschmidt, and P. A. Griffiths. Exterior Differential Systems. Springer, 2011.
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Gu, Chaohao, Marcel Berger, and Robert L. Bryant. Differential Geometry and Differential Equations Proceedings of a Symposium, held in Shanghai, June 21 - July 6, 1985. Springer, 2006.
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Bao, D., R. L. Bryant, S. -. S. Chern, and Z. Shen, eds. A Sampler of Riemann-Finsler Geometry. Vol. 50. Cambridge University Press, 2004.
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Bao, D., R. L. Bryant, S. -. S. Chern, and Z. Shen, eds. A Sampler of Riemann-Finsler Geometry. Vol. 50. Cambridge University Press, 2004.
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Bryant, Robert, Phillip Griffiths, and Daniel Grossman. Exterior Differential Systems and Euler-Lagrange Partial Differential Equations. University of Chicago Press, 2003.Open Access Copy
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Bryant, R., V. Guillemin, S. Helgason, and R. O. Wells, eds. Integral Geometry. Vol. 63. Providence, RI: American Mathematical Society, 1987.
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Bryant, R., V. Guillemin, S. Helgason, and R. O. Wells, eds. Integral Geometry. Vol. 63. Providence, RI: American Mathematical Society, 1987.
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Academic Articles
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Acharya, B. S., R. L. Bryant, and S. Salamon. “A circle quotient of a G2 cone.” Differential Geometry and Its Application 73 (December 1, 2020). https://doi.org/10.1016/j.difgeo.2020.101681.Full Text Open Access Copy
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Bryant, R. L., and J. N. Clelland. “Flat metrics with a prescribed derived coframing.” Symmetry, Integrability and Geometry: Methods and Applications (Sigma) 16 (January 1, 2020). https://doi.org/10.3842/SIGMA.2020.004.Full Text Open Access Copy
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Bryant, R. L., M. G. Eastwood, A. R. Gover, and K. Neusser. “Some differential complexes within and beyond parabolic geometry.” Advanced Studies in Pure Mathematics 82, no. Differential Geometry and Tanaka Theory (November 22, 2019): 13–40.Open Access Copy Link to Item
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Bryant, R., R. Buckmire, L. Khadjavi, and D. Lind. “The origins of spectra, an organization for LGBT mathematicians.” Notices of the American Mathematical Society 66, no. 6 (June 1, 2019): 875–82. https://doi.org/10.1090/noti1890.Full Text Open Access Copy
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Bryant, R. L., L. Huang, and X. Mo. “On Finsler surfaces of constant flag curvature with a Killing field.” Journal of Geometry and Physics 116 (June 1, 2017): 345–57. https://doi.org/10.1016/j.geomphys.2017.02.012.Full Text Open Access Copy
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Bryant, R. L. “On the convex Pfaff-Darboux Theorem of Ekeland and Nirenberg,” December 22, 2015.Open Access Copy Link to Item
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Bryant, R. L. “On the conformal volume of 2-tori,” July 6, 2015.Open Access Copy Link to Item
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Bryant, R. L. “S.-S. Chern's study of almost-complex structures on the six-sphere,” May 14, 2014.Open Access Copy Link to Item
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Bryant, R. L. “Notes on exterior differential systems,” May 13, 2014.Open Access Copy Link to Item
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Bryant, R., and F. Xu. “Laplacian Flow for Closed $G_2$-Structures: Short Time Behavior,” January 11, 2011.Open Access Copy Link to Item
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Bryant, R. L. “Commentary.” Bulletin of the American Mathematical Society 46, no. 2 (April 1, 2009): 177–78. https://doi.org/10.1090/S0273-0979-09-01248-8.Full Text
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Bryant, R. L. “Gradient Kähler Ricci solitons.” Astérisque, no. 321 (2008): 51–97.Open Access Copy Link to Item
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Bryant, R. L., G. Manno, and V. S. Matveev. “A solution of a problem of Sophus Lie: Normal forms of two-dimensional metrics admitting two projective vector fields.” Mathematische Annalen 340, no. 2 (2008): 437–63. https://doi.org/10.1007/s00208-007-0158-3.Full Text Open Access Copy
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BRYANT, R. L. “Conformal geometry and 3-plane fields on 6-manifolds.” Rims Kokyuroku 1502 (Developments of Cartan Geometry and Related Mathematical Problems) (July 2006): 1–15.Open Access Copy Link to Item
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Bryant, R. L. “SO(n)-Invariant special Lagrangian submanifolds of ℂ n+1 with fixed loci.” Chinese Annals of Mathematics. Series B 27, no. 1 (January 1, 2006): 95–112. https://doi.org/10.1007/s11401-005-0368-5.Full Text Open Access Copy
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Bryant, R. L. “On the geometry of almost complex 6-manifolds.” Asian Journal of Mathematics 10, no. 3 (January 1, 2006): 561–605. https://doi.org/10.4310/AJM.2006.v10.n3.a4.Full Text
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Bryant, Robert, and Dan Freed. “Shiing-Shen Chern.” Physics Today 59, no. 1 (January 2006): 70–72. https://doi.org/10.1063/1.2180187.Full Text
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Bryant, R. L. “Real hypersurfaces in unimodular complex surfaces,” July 27, 2004.Open Access Copy Link to Item
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Bryant, R., H. Edelsbrunner, P. Koehl, and M. Levitt. “The area derivative of a space-filling diagram.” Discrete and Computational Geometry 32, no. 3 (January 1, 2004): 293–308. https://doi.org/10.1007/s00454-004-1099-1.Full Text
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Bryant, R. L. “Some remarks on Finsler manifolds with constant flag curvature.” Houston Journal of Mathematics 28, no. 2 (January 1, 2002): 221–62.Open Access Copy Link to Item
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Bryant, R. I. “On Surfaces with Prescribed Shape Operator.” Results in Mathematics 40, no. 1–4 (October 1, 2001): 88–121. https://doi.org/10.1007/BF03322701.Full Text
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Bryant, R. L. “Bochner-kähler metrics.” Journal of the American Mathematical Society 14, no. 3 (July 1, 2001): 623–715. https://doi.org/10.1090/S0894-0347-01-00366-6.Full Text Open Access Copy
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Bryant, R. L. “Rigidity and quasi-rigidity of extremal cycles in Hermitian symmetric spaces,” March 5, 2001.Open Access Copy Link to Item
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Bryant, R. “Recent advances in the theory of holonomy.” Asterisque 266 (December 1, 2000): 351–74.Open Access Copy
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Bryant, R. L. “Harmonic morphisms with fibers of dimension one.” Communications in Analysis and Geometry 8, no. 2 (January 1, 2000): 219–65. https://doi.org/10.4310/CAG.2000.v8.n2.a1.Full Text Open Access Copy
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Bryant, R. L. “Calibrated Embeddings in the Special Lagrangian and Coassociative Cases.” Annals of Global Analysis and Geometry 18, no. 3–4 (January 1, 2000): 405–35. https://doi.org/10.1023/a:1006780703789.Full Text Open Access Copy
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Bryant, R. “Élie Cartan and geometric duality.” Journées Élie Cartan 1998 Et 1999 16 (2000): 5–20.Open Access Copy
- Bryant, RL. "Calibrated embeddings in the special Lagrangian and coassociative cases." Annals of Global Analysis and Geometry 18, no. 3-4 (2000): 405-435. Open Access Copy
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Bryant, R. L. “Some examples of special Lagrangian Tori.” Advances in Theoretical and Mathematical Physics 3, no. 1 (January 1, 1999): 83–90. https://doi.org/10.4310/ATMP.1999.v3.n1.a2.Full Text Open Access Copy
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Bryant, R. L., and E. Sharpe. “D-branes and Spinc structures.” Physics Letters, Section B: Nuclear, Elementary Particle and High Energy Physics 450, no. 4 (January 1, 1999): 353–57. https://doi.org/10.1016/S0370-2693(99)00161-6.Full Text Open Access Copy
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Bryant, R. L. “Projectively flat finsler 2-spheres of constant curvature.” Selecta Mathematica, New Series 3, no. 2 (January 1, 1997): 161–203. https://doi.org/10.1007/s000290050009.Full Text Open Access Copy
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Bryant, R., P. Griffiths, and L. Hsu. “Hyperbolic exterior differential systems and their conservation laws, part II.” Selecta Mathematica, New Series 1, no. 2 (September 1, 1995): 265–323. https://doi.org/10.1007/BF01671567.Full Text
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Bryant, Robert L., and Phillip A. Griffiths. “Characteristic cohomology of differential systems. I. General theory.” Journal of the American Mathematical Society 8, no. 3 (September 1, 1995): 507–507. https://doi.org/10.1090/s0894-0347-1995-1311820-x.Full Text
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Bryant, R., P. Griffiths, and L. Hsu. “Hyperbolic exterior differential systems and their conservation laws, part I.” Selecta Mathematica, New Series 1, no. 1 (March 1, 1995): 21–112. https://doi.org/10.1007/BF01614073.Full Text
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Bryant, R. L., and P. A. Griffiths. “Characteristic cohomology of differential systems II: Conservation laws for a class of parabolic equations.” Duke Mathematical Journal 78, no. 3 (January 1, 1995): 531–676. https://doi.org/10.1215/S0012-7094-95-07824-7.Full Text
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Bryant, R. L., and L. Hsu. “Rigidity of integral curves of rank 2 distributions.” Inventiones Mathematicae 114, no. 1 (December 1, 1993): 435–61. https://doi.org/10.1007/BF01232676.Full Text
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Bryant, R. L. “Some remarks on the geometry of austere manifolds.” Boletim Da Sociedade Brasileira De Matemática 21, no. 2 (September 1, 1991): 133–57. https://doi.org/10.1007/BF01237361.Full Text
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Bryant, R. L., and S. M. Salamon. “On the construction of some complete metrics with exceptional holonomy.” Duke Mathematical Journal 58, no. 3 (January 1, 1989): 829–50. https://doi.org/10.1215/S0012-7094-89-05839-0.Full Text
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Bryant, R., and R. Harvey. “Submanifolds in hyper-Kähler geometry.” Journal of the American Mathematical Society 2, no. 1 (January 1, 1989): 1–31. https://doi.org/10.1090/S0894-0347-1989-0953169-8.Full Text
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Bryant, R. L. “Metrics with exceptional holonomy.” Ann. of Math. (2) 126, no. 3 (1987): 525–76.
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Bryant, Robert, and Phillip Griffiths. “Reduction for Constrained Variational Problems and � κ 2 2 ds.” American Journal of Mathematics 108, no. 3 (June 1986): 525–525. https://doi.org/10.2307/2374654.Full Text
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Bryant, R. L. “Lie groups and twlstor spaces.” Duke Mathematical Journal 52, no. 1 (January 1, 1985): 223–61. https://doi.org/10.1215/S0012-7094-85-05213-5.Full Text
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Bryant, R. L. “Minimal surfaces of constant curvature in sn.” Transactions of the American Mathematical Society 290, no. 1 (January 1, 1985): 259–71. https://doi.org/10.1090/S0002-9947-1985-0787964-8.Full Text
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Bryant, R. L. “A duality theorem for willmore surfaces.” Journal of Differential Geometry 20, no. 1 (January 1, 1984): 23–53. https://doi.org/10.4310/jdg/1214438991.Full Text
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Berger, E., R. Bryant, and P. Griffiths. “The Gauss equations and rigidity of isometric embeddings.” Duke Mathematical Journal 50, no. 3 (January 1, 1983): 803–92. https://doi.org/10.1215/S0012-7094-83-05039-1.Full Text
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Bryant, R. L., P. A. Griffiths, and D. Yang. “Characteristics and existence of isometric embeddings.” Duke Mathematical Journal 50, no. 4 (January 1, 1983): 893–994. https://doi.org/10.1215/S0012-7094-83-05040-8.Full Text
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Bryant, R. L. “Conformal and minimal immersions of compact surfaces into the 4-sphere.” Journal of Differential Geometry 17, no. 3 (January 1, 1982): 455–73. https://doi.org/10.4310/jdg/1214437137.Full Text
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Bryant, R. L. “Submanifolds and special structures on the octonians.” Journal of Differential Geometry 17, no. 2 (January 1, 1982): 185–232. https://doi.org/10.4310/jdg/1214436919.Full Text
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Bryant, R. L. “Holomorphic curves in lorentzian cr-manifolds.” Transactions of the American Mathematical Society 272, no. 1 (January 1, 1982): 203–21. https://doi.org/10.1090/S0002-9947-1982-0656486-4.Full Text
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Berger, E., and P. Griffiths. “Some isometric embedding and rigidity results for Riemannian manifolds.” Proc. Nat. Acad. Sci. U.S.A. 78, no. 8 (1981): 4657–60.
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Acharya, Bobby Samir, Robert L. Bryant, and Simon Salamon. “A circle quotient of a $G_2$ cone,” n.d.Open Access Copy Link to Item
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Bryant, R. L., P. Foulon, S. Ivanov, V. S. Matveev, and W. Ziller. “Geodesic behavior for Finsler metrics of constant positive flag curvature on $S^2$,” n.d.Open Access Copy Link to Item
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Bryant, R., P. Foulon, S. Ivanov, V. S. Matveev, and W. Ziller. “Geodesic behavior for Finsler metrics of constant positive flag curvature on S^2 (Accepted).” Journal of Differential Geometry, n.d.Open Access Copy Link to Item
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Bryant, Robert L. “Levi-flat Minimal Hypersurfaces in Two-dimensional Complex Space Forms.” Adv. Stud. Pure Math., 37, Math. Soc. Japan, Tokyo, 2002, 1 44, n.d.Open Access Copy Link to Item
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Bryant, Robert L. “Recent Advances in the Theory of Holonomy.” Seminaire Bourbaki 1998, no. 99 (n.d.): 351–74.Open Access Copy Link to Item
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Bryant, Robert L. “Notes on Projective, Contact, and Null Curves,” n.d.Open Access Copy Link to Item
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Bryant, Robert L. “Notes on spinors in low dimension,” n.d.Open Access Copy Link to Item
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Bryant, Robert L. “On surfaces with prescribed shape operator.” Results Math. 40 (2001), No. 1 4, 88 121, n.d.Open Access Copy Link to Item
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Bryant, Robert L., Maciej Dunajski, and Michael Eastwood. “Metrisability of two-dimensional projective structures,” n.d.Open Access Copy Link to Item
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Book Sections
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Bryant, R. “Geodesically reversible Finsler 2-spheres of constant curvature.” In Inspired by S. S. Chern---A Memorial Volume in Honor of a Great Mathematician, edited by P. A. Griffiths, 11:95–111. Hackensack, NJ: World Scientific Publishers, 2006.Open Access Copy
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Bryant, R. “Holonomy and Special Geometries.” In Dirac Operators: Yesterday and Today, edited by J. P. Bourguinon, T. Branson, A. Chamseddine, O. Hijazi, and R. Stanton, 71–90. Somerville, MA: International Press, 2005.Open Access Copy
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Bryant, R. “Pseudo-Reimannian metrics with parallel spinor fields and vanishing Ricci tensor.” In Global Analysis and Harmonic Analysis (Marseille-Luminy, 1999), edited by J. P. Bourguinon, T. Branson, and O. Hijazi, 4:53–94. Paris: Société Mathématique de France, 2000.Open Access Copy
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Bryant, R. “On extremals with prescribed Lagrangian densities.” In Manifolds and Geometry (Pisa, 1993), edited by Pd Bartolomeis, F. Tricerri, and E. Vesentini, 36:86–111. Cambridge, UK: Cambridge University Press, 1996.Open Access Copy
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Bryant, R. “Classical, exceptional, and exotic holonomies: a status report.” In Actes de La Table Ronde de Géométrie Différentielle, edited by A. Besse, 1:93–165. Paris: Société Mathématique de France, 1996.
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Bryant, R. “An introduction to Lie groups and symplectic geometry.” In Geometry and Quantum Field Theory (Park City, UT, 1991), edited by D. Freed and K. Uhlenbeck, 1:5–181. Providence, RI: American Mathematical Society, 1995.Open Access Copy
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Bryant, R., and R. B. Gardner. “Control Structures.” In Geometry in Nonlinear Control and Differential Inclusions (Warsaw, 1993), edited by B. Jakubczyk, W. Respondek, and T. Rzezuchowski, 12:111–21. Warsaw, Poland: Polish Academy of Sciences, 1995.
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Bryant, R. “Two exotic holonomies in dimension four, path geometries, and twistor theory.” In Complex Geometry and Lie Theory (Sundance, UT, 1989), edited by J. Carlson, H. Clemens, and D. Morrison, 53:33–88. Providence, RI: American Mathematical Society, 1991.
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Bryant, R. “Surfaces in conformal geometry.” In The Mathematical Heritage of Hermann Weyl (Durham, NC, 1987), edited by R. O. Wells, 48:227–40. Providence, RI: American Mathematical Society, 1988.
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Bryant, R. “Surfaces of mean curvature one in hyperbolic space.” In Théorie Des Variétés Minimales et Applications (Palaiseau, 1983–1984), 154–155:321–47. Paris: Société Mathématique de France, 1988.
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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), edited by M. Luksic, C. Martin, and W. Shadwick, 68:65–76. Providence, RI: American Mathematical Society, 1987.
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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 A. Gleason, 505–14. Providence, RI: American Mathematical Society, 1987.
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Bryant, R. “Minimal Lagrangian submanifolds of Kähler-Einstein manifolds.” In Differential Geometry and Differential Equations (Shanghai, 1985), edited by C. Gu, M. Berger, and R. L. Bryant, 1255:1–12. Berlin, Germany: Springer-Verlag, 1987.
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Bryant, R. “Minimal Lagrangian submanifolds of Kähler-Einstein manifolds.” In Differential Geometry and Differential Equations (Shanghai, 1985), edited by C. Gu, M. Berger, and R. L. Bryant, 1255:1–12. Berlin, Germany: Springer-Verlag, 1987.
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Bryant, R. “Metrics with holonomy G2 or Spin(7).” In Workshop Bonn 1984 (Bonn, 1984), edited by F. Hirzebruch, J. Schwermer, and S. Suter, 1111:269–77. Berlin, Germany: Springer, 1985.
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Bryant, R., and P. A. Griffiths. “Some observations on the infinitesimal period relations for regular threefolds with trivial canonical bundle.” In Arithmetic and Geometry, Vol. II, edited by M. Artin and J. Tate, 36:77–102. Boston, MA: Birkhäuser Boston, 1983.
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Bryant, R., S. S. Chern, and P. A. 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 W. T. Wu, 1:219–338. Beijing, PRC; New York, NY: Science Press; Gordon & Breach Science Publishers, 1982.
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Bryant, Robert L. “Nonembedding and nonextension results in special holonomy,” n.d.Open Access Copy Link to Item
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Bryant, Robert L. “Some remarks on G_2-structures,” n.d.Open Access Copy Link to Item
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Other Articles
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Bryant, Robert L. “Complex analysis and a class of Weingarten surfaces,” n.d.Open Access Copy Link to Item
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Bryant, Robert, Bobby Acharya, and Simon Salamon. “A circle quotient of a G_2 cone (Submitted),” n.d.Link to Item
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Bryant, Robert, and Jeanne Nielsen Clelland. “Flat metrics with a prescribed derived coframing (Submitted),” n.d.Link to Item
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Bryant, Robert. “Notes on Projective, Contact, and Null Curves,” n.d.Link to Item
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Conference Papers
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Bryant, R. L. “Geometry of manifolds with special holonomy: "100 years of holonomy".” In 150 Years of Mathematics at Washington University in St. Louis, edited by G. R. Jensen and S. G. Krantz, 395:29–38. AMER MATHEMATICAL SOC, 2006.Link to Item
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Bryant, Robert L. “Second order families of special Lagrangian 3-folds.” In Perspectives in Riemannian Geometry, edited by V. Apostolov, A. Dancer, N. Hitchin, and M. Wang, 40:63–98. AMER MATHEMATICAL SOC, 2006.Open Access Copy Link to Item
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BRYANT, R., P. GRIFFITHS, and L. HSU. “TOWARD A GEOMETRY OF DIFFERENTIAL-EQUATIONS.” In Geometry, Topology & Physics, edited by S. T. Yau, 4:1–76. INTERNATIONAL PRESS INC BOSTON, 1995.Link to Item
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- Teaching & Mentoring
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Recent Courses
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Advising & Mentoring
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Anuk Dayaprema, Duke undergraduate
Eric Lin, Duke undergraduate
Yuanling Wang, Duke undergraduate
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Teaching Activities
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Math 323S: Euclidean and Non-Euclidean Geometry
Math 421: Differential Geometry
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Math 323S: Euclidean and Non-Euclidean Geometry
- Scholarly, Clinical, & Service Activities
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Presentations & Appearances
- The geometry of pseudoholomorphic curves in the 6-sphere. Special Holonomy in Geometry, Analysis, and Physics: Progress and Open Problems. Duke University. September 18, 2020 2020
- An Overview of the Progress and Goals of the Special Holonomy Simons Collaboration. Fourth Annual Meeting of the Simons Collaboration on Special Holonomy. Simons Foundation. September 9, 2020 2020
- On solitons for the closed G2-Laplacian flow. Special Session on the Geometry of Differential Equations. Joint Mathematics Meetings. January 17, 2020 2020
- An Overview of the Progress and Goals of the Special Holonomy Simons Collaboration. Third Annual Meeting of the Simons Collaboration on Special Holonomy. Simons Foundation. September 12, 2019 2019
- On solitons for the G_2 –Laplacian flow . LG&TBQ Conference. University of Michigan. June 11, 2019 2019
- Limits, Bubbles, and Singularities: An introduction to the fundamental ideas of Karen Uhlenbeck. The 2019 Abel Prize Ceremony Lectures. Norwegian Academy of Science and Letters. May 22, 2019 - May 22, 2019 2019
- 2019 Porcelli Lectures by Robert Bryant. Porcelli Lectures. Louisiana State University. March 28, 2019 - March 29, 2019 2019
- Algebraically Special Metrics with Special Holonomy. Conference on Differential Geometry in the Large. MATRIX. February 11, 2019 - February 11, 2019 2019
- Solitons for the closed G_2-Laplacian Flow. Conference on Differential Geometry in the Large. MATRIX. February 8, 2019 2019
- The Best Possible Shapes of Surfaces. Masaryk University Seminar Series in Mathematics, Physics, and Computer Science. Masaryk University, Brno, CZ. December 12, 2018 2018
- An introduction to Lie groups, symmetries, and symplectic geometry. Gulbenkian Summer School in Differential Geometry. Gulbenkian Foundation, LISBON. July 23, 2018 - July 27, 2018 2018
- Finsler metrics with constant positive flag curvature and holonomy. New Methods in Finsler Geometry. Clay Mathematics Institute. May 22, 2018 2018
- On self-dual curves. Griffiths Conference 2018. University of Miami. March 2, 2018 2018
- From Mechanics, to Algebra, to Geometry: The Notion of Holonomy. McKnight Zame Lecture in Mathematics. University of Miami. March 1, 2018 2018
- The concept of Holonomy---its history and recent developments. AMS Retiring Presidential Address. American Mathematical Society. January 13, 2018 2018
- Algebraically Constrained Special Holonomy Metrics and Second-order Associative 3-folds. Riemannian Geometry Past, Present, and Future: an Homage to Marcel Berger. Institute des Hautes Études Scientifiques. December 6, 2017 2017
- Algebraically special associative submanifolds and special holonomy metrics. Special Holonomy: Progress and Open Problems 2017. Simons Center for Geometry and Physics. September 10, 2017 2017
- Symmetry and G-structures. Topological and Geometric Methods in QFT. University of Montana in Bozeman Mathematics. July 31, 2017 2017
- Recent progress on manifolds with special holonomy. Pan-African Congress of Mathematicians 2017. Mohammed V University, Rabat. July 7, 2017 2017
- Curvature-homogeneous metrics in dimension 3.. Colorado University Mathematics Colloquium. Colorado University-Boulder Mathematics. May 2, 2017 2017
- On the geometry of geodesics on Finsler surfaces. Swarthmore Dresden Lectures (2016–17). Swarthmore College Mathematics Department. April 25, 2017 2017
- The idea of holonomy. Swarthmore Dresden Lectures (2016–17). Swarthmore College Mathematics Department. April 24, 2017 2017
- Engel structures, rigid curves, and compatible complex and symplectic structcures. AIM Workshop on Engel Structures. American Institute of Mathematics. April 20, 2017 2017
- Finsler Surfaces of Constant Curvature. First Annual Meeting of the Indian Mathematics Consortium. The Indian Mathematics Consortium. December 14, 2016 2016
- On families of special holonomy metrics defined by algebraic curvature conditions. Inaugural Conference of the Simons Collaboration "Special Holonomy in Geometry, Analysis, and Physics". Simons Center for Geometry and Physics. September 6, 2016 2016
- Integration techniques for exterior differential systems I & II. London Mathematical Society -- EPSRC Durham Symposium Geometric and Algebraic Aspects of Integrability. Durham University. July 27, 2016 2016
- On curvature-homogeneous metrics in dimension 3. "Differential Geometry in the Large (Conference in honor of Wolfgang Meyer's 80th birthday). Università degli studi Firenze. July 11, 2016 2016
- Curvature-homogeneous metrics in dimension 3. Stony Brook University Colloquium Series. Stony Brook University Mathematics Department. April 28, 2016 2016
- The geometry and dynamics of uniformly periodic recursion relations. Vanderbilt University Mathematics Colloquium Series. Vanderbilt University Mathematics Department. April 21, 2016 2016
- The geometry and dynamics of periodic equi-areal sequences. Tulane Colloquia in Mathematics. Tulane University Mathematics Department. February 25, 2016 2016
- Beyond Holonomy: Constrained Structure Equations. IHP conference "Relativity and Geometry" in memorial to André Lichnerowicz (in honor of his 100th Birthday). Institut Henri Poincaré, Paris, France. December 14, 2015 2015
- On curvature-homogeneous 3-manifolds. Baltimore-Washington Metro Area Differential Geometry Seminar. Howard University. October 24, 2015 2015
- The idea of holonomy. Public Lecture celebrating the 200th anniversary of George Boole. University College Cork, Cork, Ireland. October 12, 2015 2015
- The geometry of periodic equi-Poisson sequences. Colloquium. University of California, Irvine, Mathematics Department. May 29, 2015 2015
- The geometry of equi-areal sequences. Geometry Topology Seminar. North Carolina State University Mathematics Department. January 29, 2015 2015
- G-structures with prescribed geometry. The 35th Winter School in GEOMETRY AND PHYSICS, Srní, Czech Republic . January 18, 2015 - January 20, 2015 2015
- Some geometric constructions of holonomy plane fields and their analysis. IHP Workshop "Equivalence, invariants, and symmetries of vector distributions and related structures: from Cartan to Tanaka and beyond". Institut Henri Poincaré, Paris France. December 10, 2014 2014
- Some exceptional geometry of rolling surfaces. AMS Southeastern Regional Meeting, Special Session "Exceptional Groups in Physics, Algebra, and Geometry". UNC Greensboro. November 9, 2014 2014
- Convex billiards and non-holonomic systems. Fifty-First Annual DeLong Lectures. University of Colorado at Boulder . October 14, 2014 2014
- The idea of holonomy. Fifty-First Annual DeLong Lectures. University of Colorado at Boulder. October 13, 2014 2014
- Riemannian manifolds with special holonomy and special curvature. Simons Center program "G2 manifolds". Simons Center for Geometry and Physics . September 30, 2014 2014
- On G_2 and complex and almost-complex structures on 6-manifolds. July 14, 2014 2014
- On G_2 and complex and almost-complex structures on 6-manifolds. University College London. July 14, 2014 2014
- The Geometry of Special Holonomy Metrics. July 7, 2014 - July 11, 2014 2014
- The geometry of periodic equi-areal sequences. June 5, 2014 2014
- Existence and Non-Existence of Canonical Connections. June 3, 2014 2014
- Differential Systems and Holonomy. May 1, 2014 2014
- Rolling surfaces and exceptional geometry. April 11, 2014 2014
- The geometry of rolling surfaces and non-holonomic mechanics. March 21, 2014 2014
- Exterior Differential Systems and Lie Theory, IV: Examples and Applications. December 12, 2013 2013
- Exterior Differential Systems and Lie Theory, II: The basics of Cartan-Kähler Theory. December 11, 2013 2013
- Exterior Differential Systems and Lie Theory, III: The structure theory and existence. December 10, 2013 2013
- Exterior Differential Systems and Lie Theory, I: Introduction. December 9, 2013 2013
- Finsler geometry and manifolds of special holonomy. November 20, 2013 2013
- Prescribed curvature in Finsler geometry and PDE. November 20, 2013 2013
- Finsler spaces of constant flag curvature. November 18, 2013 2013
- Riemann-Finsler geometry and the Method of Equivalence. November 15, 2013 2013
- The geometry of equi-Poisson sequences. November 8, 2013 2013
- The exceptional geometry of binary sextics. November 5, 2013 2013
- Recent developments in special holonomy manifolds. November 1, 2013 2013
- The geometry of rolling surfaces and non-holonomic mechanics. November 1, 2013 2013
- Finsler manifolds of constant flag curvature. October 31, 2013 2013
- The origins of Finsler geometry in the calculus of variations. October 31, 2013 2013
- The geometry of calibrations. October 24, 2013 2013
- The geometry of equi-Poisson sequences. October 17, 2013 2013
- Convex Billiards and nonholonomic systems. October 9, 2013 2013
- Recent advances in the geometry of PDE. October 3, 2013 2013
- The Affine Bonnet Problem. October 1, 2013 2013
- On the geometry of rolling surfaces. September 17, 2013 2013
- A visit to the Finsler world. September 13, 2013 2013
- The affine Bonnet Problem. September 10, 2013 2013
- Convex Billiards and nonholonomic systems. September 6, 2013 2013
- Introduction to Holonomy, II. May 29, 2013 2013
- Introduction to Holonomy, I. May 28, 2013 2013
- Parking Cars, Rolling Balls, and Falling Cats: The Concept of Holonomy. May 22, 2013 2013
- Control theory, rolling surfaces, and the exceptional group G_2. April 8, 2013 2013
- Convex billiards and nonholonomic systems. November 1, 2012 2012
- Geometry Old and New: From Euclid to String Theory. November 1, 2012 2012
- On the local classification of ambiKähler structures in dimension 4. October 27, 2012 2012
- Geometry Old and New: From Euclid to String Theory. September 29, 2012 2012
- On normal forms for Pfaffian systems and their application. September 12, 2012 2012
- Some geometry of characteristic cohomology. January 23, 2012 2012
- Applications of Cartan's generalization of Lie's Third Theorem. June 13, 2011 2011
- On the affine Bonnet problem. May 17, 2011 2011
- On the affine Bonnet problem. January 24, 2011 2011
- The Affine Bonnet Problem. December 16, 2010 2010
- Cartan's Generalization of Lie's Third Fundamental Theorem. December 15, 2010 2010
- A visit to the Finsler world. December 13, 2010 2010
- Invariants of projective structures on surfaces and some applications. November 19, 2010 2010
- The Affine Bonnet Problem. November 14, 2010 2010
- The Affine Bonnet Problem. October 22, 2010 2010
- The Affine Bonnet Problem. October 17, 2010 2010
- The idea of Holonomy. October 14, 2010 2010
- On the life and work of S.-S. Chern. August 19, 2010 2010
- A visit to the Finsler world. June 2, 2010 2010
- On the geometry of projective surfaces. May 25, 2010 2010
- Auf Wiedersehen Surfaces, Revisited. March 10, 2010 2010
- The nearest way: from lines to geometry. May 28, 2009 2009
- The infinite groupoids of Lie and Cartan. May 23, 2009 2009
- Involutive Rational Normal Structures. May 12, 2009 2009
- Auf Wiedersehen Surfaces, Revisited. April 3, 2009 2009
- On Cartan's generalization of Lie's Third Theorem. December 17, 2008 2008
- On natural equations for metrics and potentials in dimension 3. November 24, 2008 2008
- Cartan's Generalization of Lie's Third Theorem. November 13, 2008 2008
- Riemannian Submersions as PDE. October 27, 2008 2008
- Involutive Rational Normal Structures. October 17, 2008 2008
- Geometry on moduli spaces of rational curves, III. September 29, 2008 2008
- Geometry on moduli spaces of rational curves, II. September 15, 2008 2008
- Geometry on moduli spaces of rational curves, I. September 8, 2008 2008
- Riemannian Submersions as PDE. September 1, 2008 2008
- The idea of holonomy. August 7, 2008 2008
- Involutive rational normal structures. August 4, 2008 2008
- The geometry of Riemannian submersions and foliations. June 6, 2008 2008
- Geometric flows and special holonomy. June 5, 2008 2008
- Riemannian Submersions as PDE. May 5, 2008 2008
- Riemannian Submersions as PDE. April 25, 2008 2008
- The Hessian representation problem. April 24, 2008 2008
- Geometric flows and special holonomy. April 23, 2008 2008
- The unreasonable effectiveness of geometric methods. April 22, 2008 2008
- Riemannian Submersions as PDE. February 2, 2008 2008
-
Service to the Profession
- Member. Search Advisory Committee for the Assistant Director of the MPS Directorate. National Science Foundation. February 2020 - June 2020 2020
- Member. US National Committee for Mathematics. National Academy of Sciences. January 29, 2019 - December 31, 2021 2019 - 2021
- Section Chair of Section 11 (Mathematics). National Academy of Sciences. May 2018 - May 2021 2018 - 2021
- Member. Scientific Advisory Board. Berlin Mathematical School. 2018 2018
- Immediate Past President. American Mathematical Society. February 2017 - February 2018 2017 - 2018
- Chair. Search Committee for new Director of the Division of Mathematical Sciences. National Science Foundation. January 2017 - June 2017 2017
- Trustee. Board of Trustees. The EDGE Foundation. January 2017 2017
- Chair. Scientific Council. Fondation Mathématique Jacques Hadamard. March 2016 - March 2020 2016 - 2020
- Member. Advisory Board. Project Euclid. 2016 2016
- President of the American Mathematical Society. American Mathematical Society. February 1, 2015 - January 31, 2017 2015 - 2017
- Member. Mathematics and Physical Sciences Advisory Committee. National Science Foundation. October 2014 - March 2021 2014 - 2021
- Member, Class I Membership Committee. National Academy of Sciences. November 15, 2013 - November 15, 2014 2013 - 2014
- Member : Scientific Committee of the IHÉS. June 1, 2013 2013
- Member : StatsNSF. November 1, 2012 - July 2013 2012 - 2013
- Chair of Membership Committee. Class I, Section 1 (Mathematics). American Academy of Arts and Sciences. July 2012 - June 2018 2012 - 2018
- Chair : 2014 Chern Medal Committee of the International Mathematical Union. June 1, 2012 - August 15, 2014 2012 - 2014
- Co-Organizer : Chern Centennial Conference. October 24, 2011 - November 4, 2011 2011
- Chair : Section I:1 (Mathematics and Statistics) panel for 2014 AAAS elections. June 1, 2011 2011
- Exterior Member : Academic Council of the Institute Henri Poincaré. July 1, 2010 2010
- Member : Board of Trustees of the Banff International Research Station. July 1, 2009 - July 31, 2013 2009 - 2013
- Deputy Chair, Chair, then Program Chair : Executive Committee of the Golden Section of the MAA. March 1, 2008 - February 28, 2011 2008 - 2011
- Member : International Committee for the National Mathematics Centre of Nigeria. January 1, 2008 2008
- Member, Organizing Committee : Bay Area Differential Geometry Seminar. 2008 - 2013 2008 - 2013
- Editor. Communications in Analysis and Geometry. 2003 2003
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Service to Duke
- Duke University. President's Council on Black Affairs. July 2019 - June 2022 2019 - 2022
- Ombud. Duke Department of Mathematics. July 2019 2019
- Academic Council of Arts and Sciences. August 2018 - May 2020 2018 - 2020
- Advisory Committee on Distinguished Professorships in Arts and Sciences . July 2016 - June 2018 2016 - 2018
- Provost Advisory Committee on Appointments, Promotion, and Tenure. July 2016 - December 2019 2016 - 2019
- Chamber Arts Society of Durham. July 1, 2013 2013
Some information on this profile has been compiled automatically from Duke databases and external sources. (Our About page explains how this works.) If you see a problem with the information, please write to Scholars@Duke and let us know. We will reply promptly.
