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Robert Bryant

Phillip Griffiths Professor of Mathematics
Mathematics
Box 90320, Durham, NC 27708-0320
120 Science Drive, Durham, NC 27708

Overview


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.

Office Hours


Wednesdays, 10:00AM-12noon ET, and by appointment (please write to chair@math.duke.edu for appointments).

Current Appointments & Affiliations


Phillip Griffiths Professor of Mathematics · 2013 - Present Mathematics, Trinity College of Arts & Sciences
Professor in the Department of Mathematics · 1987 - Present Mathematics, Trinity College of Arts & Sciences

Education, Training & Certifications


University of North Carolina, Chapel Hill · 1979 Ph.D.
North Carolina State University · 1974 B.S.