Hubert Bray, Professor of Mathematics and Physics
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 largescale 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.  Contact Info:
Teaching (Fall 2018):
 MATH 89S.02, FIRSTYEAR SEMINAR (TOP)
Synopsis
 Physics 227, MW 01:25 PM02:40 PM
 MATH 112L.001, LABORATORY CALCULUS II
Synopsis
 West Duke 105, MW 04:55 PM05:45 PM; French Sci 2231, Th 11:45 AM01:00 PM
 MATH 112L.002, LABORATORY CALCULUS II
Synopsis
 West Duke 105, MW 12:00 PM12:50 PM; West Duke 202, Th 11:45 AM01:00 PM
Teaching (Spring 2019):
 MATH 112L.06L, LABORATORY CALCULUS II
Synopsis
 Physics 130, F 10:05 AM11:20 AM
 MATH 112L.07L, LABORATORY CALCULUS II
Synopsis
 Physics 130, F 10:05 AM11:20 AM
 MATH 112L.08L, LABORATORY CALCULUS II
Synopsis
 Physics 130, F 10:05 AM11:20 AM
 MATH 190.01, SPECIAL TOPICS IN MATH
Synopsis
 Physics 235, TuTh 10:05 AM11:20 AM
 (also crosslisted as ENGLISH 1901.01, ISS 190.01)
 Office Hours:
 Mondays, 4:30  6:30 p.m.
 Education:
Ph.D.  Stanford University  1997 
B.A.  Rice University  1992 
 Specialties:

Geometry
Analysis Mathematical Physics
 Research Interests: Geometric Analysis, General Relativity, Theoretical Astrophysics
 Keywords:
Analysis • General relativity (Physics) • Geometric analysis • Geometry • Mathematical physics • Theoretical astrophysics
 Curriculum Vitae
 Current Ph.D. Students
(Former Students)
 Benjamin Hamm
 Henri Roesch
 Postdocs Mentored
 Representative Publications
(More Publications)
 MartinezMedina, LA; Bray, HL; Matos, T, On wave dark matter in spiral and barred galaxies,
Journal of Cosmology and Astroparticle Physics, vol. 2015 no. 12
(December, Accepted, 2015),
pp. 025025 [arXiv:1505.07154], [1505.07154], [doi]
 Bray, H; Goetz, AS, Wave Dark Matter and the TullyFisher Relation
(Preprint, September, 2014) [arXiv:1409.7347], [7347] [abs]
 Bray, HL; Jauregui, JL; Mars, M, Time Flat Surfaces and the Monotonicity of the Spacetime Hawking Mass II,
Annales Henri Poincaré, vol. 17 no. 6
(July 26, 2015),
pp. 14571475, Springer Basel, ISSN 14240637 [arXiv:1402.3287 [math.DG]], [3287], [doi] [abs]
 Bray, HL; Jauregui, JL, Time Flat Surfaces and the Monotonicity of the Spacetime Hawking Mass,
Communications in Mathematical Physics, vol. 335 no. 1
(April, 2014),
pp. 285307, ISSN 00103616 [arXiv:1310.8638 [math.DG]], [8638], [doi]
 Bray, HL; Jauregui, JL, On curves with nonnegative torsion,
Archiv der Mathematik, vol. 104 no. 6
(2015),
pp. 561575, ISSN 0003889X [arXiv:1312.5171 [math.DG]], [c8d239381b86496b96d95ff26f1061eb], [doi]
 Bray, HL; Parry, AR, Modeling wave dark matter in dwarf spheroidal galaxies,
Journal of Physics: Conference Series, vol. 615
(2015), ISSN 17426588 [Gateway.cgi], [doi]
 Bray, H, On Wave Dark Matter, Shells in Elliptical Galaxies, and the Axioms of General Relativity
(Preprint, December 22, 2012) [pdf] [abs]
 Bray, HL, On Dark Matter, Spiral Galaxies, and the Axioms of General Relativity,
AMS Contemporary Mathematics Volume, vol. 599 no. Geometric Analysis, Mathematical Relativ
(2013), American Mathematical Society [arXiv:1004.4016], [html]
 Bray, H, On the Positive Mass, Penrose, and ZAS Inequalities in General Dimension,
in Surveys in Geometric Analysis and Relativity in Honor of Richard Schoen’s 60th Birthday, edited by Bray, H; Minicozzi, W
(2011), Higher Education Press and International Press, Beijing and Boston [arXiv:1101.2230v1], [2230] [author's comments]
 Bray, HL; Khuri, MA, P. D. E. 'S which imply the penrose conjecture,
Asian Journal of Mathematics, vol. 15 no. 4
(December, 2011),
pp. 557610, International Press, ISSN 10936106 [pdf] [abs] [author's comments]
 Bray, HL; Khuri, MA, A jang equation approach to the penrose inequality,
Discrete and Continuous Dynamical Systems Series A, vol. 27 no. 2
(June, 2010),
pp. 741766, ISSN 10780947 [arXiv:0910.4785v1], [doi] [abs]
 Bray, H; Brendle, S; Eichmair, M; Neves, A, AreaMinimizing Projective Planes in 3Manifolds,
Communications on Pure and Applied Mathematics, vol. 63 no. 9
(2010),
pp. 12371247, ISSN 00103640 [arXiv:0909.1665v1], [doi] [abs]
 Bray, H; Brendle, S; Neves, A, Rigidity of areaminimizing twospheres in threemanifolds,
Communications in Analysis and Geometry, vol. 18 no. 4
(2010),
pp. 821830, ISSN 10198385 [arXiv:1002.2814], [doi] [abs]
 Bray, HL; Jauregui, JL, A geometric theory of zero area singularities in general relativity,
Asian Journal of Mathematics, vol. 17 no. 3
(September, 2013),
pp. 525560, ISSN 10936106 [arXiv:0909.0522v1], [doi] [abs]
 Bray, HL; Lee, DA, On the Riemannian Penrose inequality in dimensions less than eight,
Duke Mathematical Journal, vol. 148 no. 1
(2009),
pp. 81106, ISSN 00127094 [arXiv:0705.1128v1], [pdf], [doi] [abs]
 Bray, H; Miao, P, On the capacity of surfaces in manifolds with nonnegative scalar curvature,
Inventiones Mathematicae, vol. 172 no. 3
(June, 2008),
pp. 459475, ISSN 00209910 [arXiv:0707.3337v1], [doi] [abs]
 Bray, H; Hayward, S; Mars, M; Simon, W, Generalized inverse mean curvature flows in spacetime,
Communications in Mathematical Physics, vol. 272 no. 1
(May, 2007),
pp. 119138, ISSN 00103616 [arXiv:grqc/0603014v1], [doi] [abs]
 Bray, HL; Neves, A, Classification of Prime 3Manifolds with Yamabe Invariant Greater than RP^3,
Annals of Mathematics, vol. 159 no. 1
(January, 2004),
pp. 407424 [p09] [abs]
 Bray, H, The Positve Energy Theorem and Other Inequalities,
in The Encyclopedia of Mathematical Physics
(2005)
 H.L. Bray, A Family of Quasilocal Mass Functionals with Monotone Flows,
in Proceedings of the 14th International Congress on Mathematical Physics, Lisbon, Portugal, 2003, edited by JeanClaude Zambrini
(2003) [Family%20of%20Quasilocal%20Mass%20Functionals%20with%20Monotone%20Flows&f=false]
 Bray, H; Finster, F, Curvature estimates and the Positive Mass Theorem,
Communications in Analysis and Geometry, vol. 10 no. 2
(2002),
pp. 291306 [arXiv:math/9906047v3] [abs]
 Bray, HL; Iga, K, Superharmonic Functions in R^n and the Penrose Inequality in General Relativity,
Communications in Analysis and Geometry, vol. 10 no. 5
(2002),
pp. 9991016
 Bray, H; Morgan, F, An isoperimetric comparison theorem for schwarzschild space and other manifolds,
Proceedings of the American Mathematical Society, vol. 130 no. 5
(2002),
pp. 14671472 [pdf], [doi] [abs]
 Bray, HL, Proof of the Riemannian Penrose Inequality Using the Positive Mass Theorem,
Journal of Differential Geometry, vol. 59 no. 2
(October, 2001),
pp. 177267 [arXiv:math/9911173v1], [pdf], [doi] [abs]
 Bray, H; Schoen, RM, Recent Proofs of the Riemannian Penrose Conjecture,
in Current Developments in Mathematics
(1999),
pp. 136, International Press
 H.L. Bray, The Positve Energy Theorem and Other Inequalities in GR,
in The Encyclopedia of Mathematical Physics
(2005)
 Bray, H; Chrusciel, PT, The Penrose Inequality,
in The Einstein Equations and the Large Scale Behavior of Gravitational Fields (50 Years of the Cauchy Problem in General Relativity), edited by Chrusciel, PT; Friedrich, HF
(2004), Birkhauser [arXiv:grqc/0312047v2]
 Bray, HL, Black Holes, Geometric Flows, and the Penrose Inequality in General Relativity,
Notices of the American Mathematical Society, vol. 49 no. 11
(2002),
pp. 13721381 [pdf]
 Bray, H, Black Holes and the Penrose Inequality in General Relativity,
in Proceedings of the International Congress of Mathematicians, Beijing, China, 2002,
Proceedings of the International Congress of Mathematicians, vol. 2
(2002),
pp. 257272 [arXiv:math/0304261v1], [0304261v1]
 Bray, H; McCormick, K; Jr, ROW; Zhou, XD, Wavelet variations on the Shannon sampling theorem,
BioSystems, vol. 34 no. 13
(1995),
pp. 249257, Elsevier Science Ireland, ISSN 03032647 [science], [doi] [abs] [author's comments]
 Bray, H, The Penrose Inequality in General Relativity and Volume Comparison Theorems Involving Scalar Curvature
(1997) (thesis, Stanford University.) [arXiv:0902.3241v1]
 Selected Invited Lectures
 The Geometry of the Universe (Research Lecture) : University of Waterloo, March 09, 2015, University of Waterloo
 Two lectures on the geometry of space and time (General audience talks), March 09, 2015, University of Waterloo [pdf]
 From Pythagoras to Einstein: The Geometry of Space and Time (General audience talk), March 09, 2015, University of Waterloo [watch]
 The Science behind "Trevor the Time Traveler” (For everyone, ages 8 and up), March 09, 2015, University of Waterloo [watch]
 The G. Milton Wing Lectures, April 23  25, 2014, University of Rochester (Series of 3 Lectures, 1 General Public, 1 Colloquium Style, 1 Research Talk) [html]
 The G. Milton Wing Lectures, Lecture 1: "From Pythagoras to Einstein: The Geometry of Space and Time", April 23, 2014, University of Rochester (Broad Audience Talk) [pdf]
 The G. Milton Wing Lectures, Lecture 2: "On Dark Matter, Galaxies, and the Large Scale Geometry of the Universe", April 24, 2014, University of Rochester (Colloquium Style Talk) [pdf]
 The G. Milton Wing Lectures, Lecture 3: "Black Holes and the Monotonicity of the Hawking Mass for Time Flat Surfaces", April 25, 2014, University of Rochester (Research Style Talk  link to paper) [pdf]
 On the Monotonicity of the Hawking Mass for Time Flat Surfaces, October 11, 2013, New York General Relativity Seminar, Columbia University (Research Talk)
 On Wave Dark Matter and the Geometry of Galaxies, May 24, 2013, JDG Conference, Lehigh University (Research Talk) [html]
 On Dark Matter, Galaxies, and the Large Scale Geometry of the Universe, February 24, 2013, The 20th Southern California Geometric Analysis Seminar, UCSan Diego (Research Talk, slides only, but video of the similar talk below is available) [pdf]
 On Dark Matter, Spiral Galaxies, and the Axioms of General Relativity, May 12, 2011, The 41st Barrett Memorial Lectures in Mathematical Relativity, University of Tennessee, Knoxville (Research Talk, with video) [available here]
 On Dark Matter, Spiral Galaxies, and the Axioms of General Relativity, April 15, 2011, The 26th Annual Geometry Festival at the University of Pennsylvania (Research Talk  slides only  100MB; the talk above was very similar and has video) [pdf]
 Dark Matter in Galaxies (Dark Matter Awareness Week talk) by Hubert Bray and Andriy Badin (Survey Talk), December 6, 2010, Duke University [video.html]
 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, December 13, 2010, University of Tennessee
 From Pythagoras to Einstein: How Geometry Describes the LargeScale Structure of the Universe (Part 1) (Broad Audience Talk), March 26, 2011, Duke University
 From Pythagoras to Einstein: How Geometry Describes the LargeScale Structure of the Universe (Part 2) (Broad Audience Talk), March 26, 2011, Duke University
 An Overview of General Relativity (Broad Audience Talk), October 3, 2008, Duke University
 What Do Black Holes and Soap Bubbles Have in Common? (Broad Audience Talk), September 21, 2007, Duke University [video.html]
 Black Holes and the Curvature of Spacetime (Broad Audience Talk), November 7, 2005, Michigan State University [html]
 Negative Point Mass Singularities in General Relativity, August, 2005, Sir Isaac Newton Institute, Cambridge, England (Research Talk) [available here]
 Generalization of the Hawking Mass, August, 2002, 50 Years of the Cauchy Problem in General Relativity, Cargese, Corsica (Research Talk) [available here]
 Proof of the Poincare Conjecture for 3Manifolds with Yamabe Invariant Greater than RP^3, August, 2002, 50 Years of the Cauchy Problem in General Relativity, Cargese, Corsica (Research Talk) [available here]
 Black Holes, the Penrose Conjecture, and Quasilocal Mass, August, 2002, 50 Years of the Cauchy Problem in General Relativity, Cargese, Corsica (Research Talk) [available here]
 Black Holes, Minimal Surfaces, and Geometric Flows, April 28, 2001, Duke Math Journal Conference, Duke University (Research Talk) [video.html]
 Quasilocal Mass and Black Holes in General Relativity, April 28, 2001, Geometry Seminar, Duke University (Research Talk) [video.html]
 Proof of the Riemannian Penrose Conjecture, June 25, 1999, Institute for Theoretical Physics, UC Santa Barbara (Research Talk) [available here]
 Selected Grant Support
 Time Flat Curves and Surfaces, Geometric Flows, and the Penrose Conjecture, National Science Foundation, DMS1406396.
 Scalar Curvature, the Penrose Conjecture, and the Axioms of General Relativity, National Science Foundation, DMS1007063.
 Geometric Analysis Applied to General Relativity, National Science Foundation, DMS0706794.
 2002  2007: Scalar Curvature, Geometric Flows, and the General Penrose Conjecture, National Science Foundation, DMS0533551 (DMS0206483 before transfered to Duke).
 1999  2002: A Continuing Investigation of the Penrose Conjecture in General Relativity, National Science Foundation, DMS9971960.
 1997  1999: Mathematical Sciences Postdoctoral Research Fellowship, National Science Foundation, DMS9706006.
 Conferences Organized
 32nd Annual Geometry Festival, Coorganizer (with Robert Bryant, Lenny Ng, Goncalo Oliveira, and Mark Stern), March 31, 2017  April 02, 2017
 Special Session in "Geometric Analysis and General Relativity", Organizer (with Otis Chodosh, Greg Galloway, and Pengzi Miao), March 2017
 AMS Special Session on Geometric Analysis, Organizer (with Andrew Cooper), November 8, 2014  November 9, 2014
 Park City Mathematics Institute Summer Program on Geometric Analysis, Organizer (with Greg Galloway, Rafe Mazzeo, and Natasa Sesum), June 30, 2013  July 20, 2013
 27th Annual Geometry Festival, Organizer (with Mark Stern, Lenny Ng, Carla Cederbaum, Luca DiCerbo, and Chris Cornwell), April 27, 2012  April 29, 2012
 Dark Matter Awareness Week, Organizer and Presenter at Duke University (along with Andriy Badin), December 6, 2010
 23rd Annual Geometry Festival, Organizer (with Benoit Charbonneau, Dick Hain, and Patrick Eberlein), April 25  27, 2008
 AIM / Stanford Relativity Workshop, Organizer (with Richard Schoen and Jim Isenberg), 2002
