- Professor of Mathematics
Mondays, 4:30 - 6:30 p.m.
Research Areas and Keywords
Geometry: Differential & Algebraic
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.
Bray, HL. "Proof of the Riemannian Penrose inequality using the positive mass theorem." Journal of Differential Geometry 59.2 (2001): 177-267.
Bray, H, McCormick, K, Jr, ROW, and Zhou, X-D. "Wavelet variations on the Shannon sampling theorem." BioSystems 34.1-3 (1995): 249-257. Full Text
From Pythagoras to Einstein: How Geometry Describes the Large-Scale Structure of the Universe (Part 1) (Broad Audience Talk). Duke University Graduate Student Recruiting Weekend. Duke University. March 26, 2011
From Pythagoras to Einstein: How Geometry Describes the Large-Scale Structure of the Universe (Part 2) (Broad Audience Talk). Duke University Graduate Student Recruiting Weekend. Duke University. March 26, 2011
From Black Holes and the Big Bang to Dark Energy and (maybe even) Dark Matter: Successes of Einstein's Theory of General Relativity (Broad Audience Talk) : 45 minutes. University of Tennessee. December 13, 2010