Isadore M. Singer (1924–2021) In Memoriam Part 2: Personal Recollections

Abstract

Department

Description

Provenance

Subjects

Citation

Published Version (Please cite this version)

10.1090/noti2573

Publication Info

Bryant, Robert, Jeff Cheeger, Phillip Griffiths, Lenore Blum, Dan Burns, Alain Connes, Harold Donnelly, David Ebin, et al. (2022). Isadore M. Singer (1924–2021) In Memoriam Part 2: Personal Recollections. Notices of the American Mathematical Society, 69(10). pp. 1–1. 10.1090/noti2573 Retrieved from https://hdl.handle.net/10161/29322.

This is constructed from limited available data and may be imprecise. To cite this article, please review & use the official citation provided by the journal.

Scholars@Duke

Bryant

Robert Bryant

Phillip Griffiths Distinguished 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.


Unless otherwise indicated, scholarly articles published by Duke faculty members are made available here with a CC-BY-NC (Creative Commons Attribution Non-Commercial) license, as enabled by the Duke Open Access Policy. If you wish to use the materials in ways not already permitted under CC-BY-NC, please consult the copyright owner. Other materials are made available here through the author’s grant of a non-exclusive license to make their work openly accessible.