2004  |  Professor of Mathematics
University of Washington 2004, PhD
CH 308C   |  907-474-1196
damaxwell@alaska.edu

I study the mathematics of general relativity, Einstein's theory of gravity. General relativity describes how all the matter in the universe bends it, and I am particularly interested in the following question: given a configuration of matter at a moment in time (e.g, a distribution of galaxies), what possible shapes of the universe are compatible with that configuration.  The question is made hard in part because the universe does not possess a good notion of a single moment in time, "right now, everywhere", and in part because the universe is allowed to ripple with gravitational waves in ways that are not determined by the stuff that is in it.  I have also published work in the broader field of geometric analysis (the study of the interaction of geometry and partial differential equations), inverse problems, and partial differential equations.

Highlighted works:

A Phase Space Approach to the Conformal Construction of Non-Vacuum Initial Data Sets in General Relativity, James Isenberg and David Maxwell, arXiv:2106.15027

Initial data in general relativity described by expansion, conformal deformation and drift,

David Maxwell, Communications in Analysis and Geometry, volume 29, 2021

Yamabe classification and prescribed scalar curvature in the asymptotically Euclidean setting,

James Dilts and David Maxwell, Communications in Analysis and Geometry, volume 26, 2018

The Conformal Method and the Conformal Thin-Sandwich Method Are the Same, David Maxwell, Classical and Quantum Gravity, volume 31, 2014