Overview
Professor Bray uses differential geometry to understand general relativity, and general relativity to motivate interesting problems in differential geometry. In 2001, he published his proof of the Riemannian Penrose Conjecture about the mass of black holes using geometric ideas related to minimal surfaces, scalar curvature, conformal geometry, geometric flows, and harmonic functions. He is also interested in the large-scale unexplained curvature of the universe, otherwise known as dark matter, which makes up most of the mass of galaxies. Professor Bray has proposed geometric explanations for dark matter which he calls "wave dark matter," which motivate very interesting questions about geometric partial differential equations.
Professor Bray has supervised 8 math Ph.D. graduates at Duke from 2006 to 2017. He is currently supervising one math Ph.D. student and one physics Ph.D. student. His most recent Ph.D. graduate, Henri Roesch, proved a Null Penrose Conjecture, open since 1973, as his thesis. While the physical motivation about the mass of black holes is the same as for the Riemannian Penrose Conjecture, the geometry involved is almost unrecognizably different, and may be viewed as a fundamental result about null geometry.
Professor Bray has supervised 8 math Ph.D. graduates at Duke from 2006 to 2017. He is currently supervising one math Ph.D. student and one physics Ph.D. student. His most recent Ph.D. graduate, Henri Roesch, proved a Null Penrose Conjecture, open since 1973, as his thesis. While the physical motivation about the mass of black holes is the same as for the Riemannian Penrose Conjecture, the geometry involved is almost unrecognizably different, and may be viewed as a fundamental result about null geometry.
Current Appointments & Affiliations
Professor of Mathematics
·
2004 - Present
Mathematics,
Trinity College of Arts & Sciences
Recent Publications
Spacetime Harmonic Functions and Applications to Mass
Other Perspectives in Scalar Curvature · February 1, 2023 In the pioneering work of Stern, level sets of harmonic functions have been shown to be an effective tool in the study of scalar curvature in dimension 3. Generalizations of this idea, utilizing level sets of so called spacetime harmonic functions as well ... Link to item CiteScalar curvature and harmonic one-forms on three-manifolds with boundary
Journal Article · November 15, 2019 Link to item CiteHarmonic Functions and The Mass of 3-Dimensional Asymptotically Flat Riemannian Manifolds
Journal Article · November 15, 2019 Link to item CiteRecent Grants
Time Flat Curves and Surfaces, Geometric Flows, and the Penrose Conjecture
ResearchPrincipal Investigator · Awarded by National Science Foundation · 2014 - 2018Scalar Curvature, the Penrose Conjecture, and the Axioms of General Relativity
ResearchPrincipal Investigator · Awarded by National Science Foundation · 2010 - 2014Geometric Analysis Applied to General Relativity
ResearchPrincipal Investigator · Awarded by National Science Foundation · 2007 - 2010View All Grants
Education, Training & Certifications
Stanford University ·
1997
Ph.D.
Rice University ·
1992
B.A.