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 …
Office Hours
Wednesdays, 10:00AM-12noon ET, and by appointment (please write to chair@math.duke.edu for appointments).
Current Appointments & Affiliations
Phillip Griffiths Distinguished 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
Recent Publications
Michael Spivak: A Memorial
Journal Article Notices of the American Mathematical Society · June 1, 2024 Full text CiteHessianizability of surface metrics
Preprint · May 11, 2024 Link to item CiteCurvature homogeneous hypersurfaces in space forms
Preprint · April 2, 2024 Open Access Link to item CiteRecent Grants
Special Holonomy In Geometry, Analysis and Physics
ResearchPrincipal Investigator · Awarded by Simons Foundation · 2020 - 2024Special Holonomy In Geometry, Analysis and Physics
ResearchPrincipal Investigator · Awarded by Simons Foundation · 2016 - 2020The Geometry of Partial Differential Equations and Applications
ResearchPrincipal Investigator · Awarded by National Science Foundation · 2013 - 2015View All Grants
Education, Training & Certifications
University of North Carolina, Chapel Hill ·
1979
Ph.D.
North Carolina State University ·
1974
B.S.