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Research Interests for Robert Bryant

Research Interests: Nonlinear Partial Differential Equations and Differential Geometry

I'm interested in the geometry of partial differential equations (as always), but, more specifically, I have been thinking about conservation laws for PDE, Finsler geometry, calibrations, holonomy, and trying to learn more about Seiberg-Witten invariants and symplectic geometry.

Keywords:
Almost complex manifolds, calibrations, CR hypersurfaces, exterior differential systems, Finsler, Geometry, Differential, Global differential geometry, solitons
Areas of Interest:

exterior differential systems
differential geometry
algebraic geometry
Finsler geometry

Recent Publications   (search)
  1. 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) [doi]
  2. 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) [doi]
  3. 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) [doi]
  4. 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 [arXiv:1405.3405], [doi[abs]
  5. 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 [doi[abs]

 

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Mathematics Department
Duke University, Box 90320
Durham, NC 27708-0320