Research Interests for Robert L 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:
calibrations, solitons, CR hypersurfaces, exterior differential systems, Finsler
Areas of Interest:

exterior differential systems
differential geometry
algebraic geometry
Finsler geometry

Recent Publications   (search)
  1. with Michael G. Eastwood, A. Rod. Gover, Katharina Neusser, Some differential complexes within and beyond parabolic geometry (Preprint, December, 2011) [arXiv:1112.2142v2] [abs]
  2. Non-embedding and non-extension results in special holonomy, in The many facets of geometry, edited by Jean-Pierre Bourguignon, Simon Salamon, and Oscar Garcia Prada (Fall, 2010), pp. 346--367, Oxford University Press, Oxford [MR2681703]
  3. with M. Dunajski, M. Eastwood, Metrisability of two-dimensional projective structures, J. Differential Geometry, vol. 83 no. 3 (2009), pp. 465--499, ISSN 0022-040X [MR2581355], [arXiv:0801.0300v1 [math.DG]] [abs]
  4. Gradient Kähler Ricci Solitons, in Géométrie différentielle, physique mathématique, mathématiques et société. I., Astérisque, vol. 321 (Spring, 2008), pp. 51--97, ISBN 978-285629-258-7 [MR2010i:53138], [math.DG/0407453] [abs]
  5. with G. Manno, V. Matveev, A solution of a problem of Sophus Lie: Normal forms of 2-dimensional metrics admitting two projective vector fields, Mathematische Annalen, vol. 340 no. 2 (Spring, 2008), pp. 437--463 [3592] [abs]