Geometric Analysis, General Relativity, Theoretical Astrophysics
Professional Experience / Employment History
Duke University
Professor, Mathematics and Physics, 2011 - present
Professor, Mathematics, 2004 - 2011
Columbia University
Associate Professor, Mathematics, 2003 - 2005 (on leave 2004 - 2005)
Massachusetts Institute of Technology
Associate Professor, Mathematics, 2003 - 2005 (on leave 2003 - 2005)
Assistant Professor, Mathematics, 1999 - 2003 (Stanford, Jan-Aug, 2002)
C. L. E. Moore Instructor, Mathematics, 1997 - 1999 (on leave 1997 - 1998)
Harvard University
NSF Fellowship Postdoc, Mathematics, 1997 - 1998
Awards, Honors, and Distinctions
Community Service Award, Duke University’s Office of Durham and Regional Affairs
Fellow of the AMS, Inaugural Class, The American Mathematical Society, January, 2013
Invited Speaker, International Congress of Mathematical Physics, Lisbon, Portugal, General Relativity section, August, 2003
Invited Speaker, International Congress of Mathematicians Satellite Conference on Differential Geometry, August, 2002
Invited Speaker, International Congress of Mathematicians, Beijing, China, Differential Geometry section, August, 2002
Sloan Research Fellowship-Mathematics, Alfred P. Sloan Foundation
Invited Speaker, Current Developments in Mathematics Conference, Harvard University, November, 1999
1997 - 1999: Mathematical Sciences Postdoctoral Research Fellowship, National Science Foundation
Bronze Medal, International Math Olympiad, Sydney, Australia, 1988
Conferences Organized
Co-organizer (with Robert Bryant, Lenny Ng, Goncalo Oliveira, and Mark Stern), 32nd Annual Geometry Festival, March 31, 2017 - April 02, 2017
Organizer (with Otis Chodosh, Greg Galloway, and Pengzi Miao), Special Session in "Geometric Analysis and General Relativity", March 2017
Organizer (with Andrew Cooper), AMS Special Session on Geometric Analysis, November 8, 2014 - November 9, 2014
Organizer (with Greg Galloway, Rafe Mazzeo, and Natasa Sesum), Park City Mathematics Institute Summer Program on Geometric Analysis, June 30, 2013 - July 20, 2013
Organizer (with Mark Stern, Lenny Ng, Carla Cederbaum, Luca DiCerbo, and Chris Cornwell), 27th Annual Geometry Festival, April 27, 2012 - April 29, 2012
Organizer and Presenter at Duke University (along with Andriy Badin), Dark Matter Awareness Week, December 6, 2010
Organizer (with Benoit Charbonneau, Dick Hain, and Patrick Eberlein), 23rd Annual Geometry Festival, April 25 - 27, 2008
Organizer (with Richard Schoen and Jim Isenberg), AIM / Stanford Relativity Workshop, 2002
Selected Recent Invited Talks
Flatly Foliated Relativity: Gravity without Gravitational Waves, University of Vienna, Austria, 1 August 2017
Flatly Foliated Relativity: Gravity without Gravitational Waves, 2 December 2016
Flatly Foliated Relativity: Gravity without Gravitational Waves, University of California, Santa Cruz, 11 May 2016
On Wave Dark Matter and the Axioms of General Relativity, Mathematics Department, University of California, Santa Cruz, 10 May 2016
From Pythagoras to Einstein: The Geometry of Space and Time (General audience talk), University of Waterloo, March 09, 2015
The Geometry of the Universe (Research Lecture) : University of Waterloo, University of Waterloo, March 09, 2015
The Science behind "Trevor the Time Traveler” (For everyone, ages 8 and up), University of Waterloo, March 09, 2015
Two lectures on the geometry of space and time (General audience talks), University of Waterloo, March 09, 2015
The G. Milton Wing Lectures, University of Rochester (Series of 3 Lectures, 1 General Public, 1 Colloquium Style, 1 Research Talk), April 23 - 25, 2014
The G. Milton Wing Lectures, Lecture 1: "From Pythagoras to Einstein: The Geometry of Space and Time", University of Rochester (Broad Audience Talk), April 23, 2014
The G. Milton Wing Lectures, Lecture 2: "On Dark Matter, Galaxies, and the Large Scale Geometry of the Universe", University of Rochester (Colloquium Style Talk), April 24, 2014
The G. Milton Wing Lectures, Lecture 3: "Black Holes and the Monotonicity of the Hawking Mass for Time Flat Surfaces", University of Rochester (Research Style Talk - link to paper), April 25, 2014
On the Monotonicity of the Hawking Mass for Time Flat Surfaces, New York General Relativity Seminar, Columbia University (Research Talk), October 11, 2013
On the Monotonicity of the Hawking Mass for Time Flat Surfaces (Research Talk), Columbia University, 11 October 2013
On Wave Dark Matter and the Geometry of Galaxies, JDG Conference, Lehigh University (Research Talk), May 24, 2013
On Wave Dark Matter and the Geometry of Galaxies (Research Talk), Lehigh University , 24 May 2013
On Dark Matter, Galaxies, and the Large Scale Geometry of the Universe, The 20th Southern California Geometric Analysis Seminar, UC-San Diego (Research Talk, slides only, but video of the similar talk below is available), February 24, 2013
On Dark Matter, Galaxies, and the Large Scale Geometry of the Universe (Research Talk), UC-San Diego, 24 February 2013
On Dark Matter, Galaxies, and the Large Scale Geometry of the Universe, Rice University, October 15, 2012
On Dark Matter, Galaxies, and the Large Scale Geometry of the Universe, Northwestern University, May 21, 2012
On Dark Matter, Galaxies, and the Large Scale Geometry of the Universe, The Center for Computational Relativity and Gravitation, Rochester Institute of Technology, May 21, 2012
On Dark Matter, Spiral Galaxies, and the Axioms of General Relativity, The 41st Barrett Memorial Lectures in Mathematical Relativity, University of Tennessee, Knoxville (Research Talk, with video), May 12, 2011
On Dark Matter, Spiral Galaxies, and the Axioms of General Relativity (Research Talk), University of Tennessee, Knoxville , 12 May 2011
On Dark Matter, Spiral Galaxies, and the Axioms of General Relativity, The 26th Annual Geometry Festival at the University of Pennsylvania (Research Talk - slides only - 100MB; the talk above was very similar and has video), April 15, 2011
On Dark Matter, Spiral Galaxies, and the Axioms of General Relativity (Research Talk), University of Pennsylvania, 15 April 2011
From Pythagoras to Einstein: How Geometry Describes the Large-Scale Structure of the Universe (Part 1) (Broad Audience Talk), 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, 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
On Dark Matter, Spiral Galaxies, and the Axioms of General Relativity, 17th Southeast Geometry Seminar, University of Tennessee, December 13, 2010
Dark Matter in Galaxies (Dark Matter Awareness Week talk) by Hubert Bray and Andriy Badin (Survey Talk), Duke University, December 6, 2010
On Dark Matter, Spiral Galaxies, and the Axioms of General Relativity, Duke University Graduate/Faculty Seminar (Broad Audience Talk) Audio only - however, a briefer version of this talk -with video- is given in the last 25 minutes of the "Dark Matter in Galaxies" Dark Matter Awareness Week lecture, September 24, 2010
On Dark Matter, Spiral Galaxies, and the Axioms of General Relativity, Geometric Analysis and General Relativity, Banff International Research Station (BIRS), June 23, 2010
On Dark Matter, Spiral Galaxies, and the Axioms of General Relativity, Southeast Geometry Conference, College of Charleston, April 24, 2010
On Dark Matter and Spiral and Elliptical Structures in Galaxies, Workshop on Dark Matter, Complex Methods, and Orbifolds in Gravitational Lensing, Petters Research Institute, Dangriga, Belize, March 20, 2010
On Dark Matter, Spiral Galaxies, and the Axioms of General Relativity, Symposium on Geometric Analysis and Mathemematical Relativity, University of Miami, February 22, 2010
Voting Rules for Democracy without Institutionalized Parties, Duke University Graduate/Faculty Seminar (Broad Audience Talk), February 05, 2010
On Dark Matter, Spiral Galaxies, and the Axioms of General Relativity, "Workshop on General Relativity," Simons Center for Geometry and Physics, SUNY - Stony Brook, November 19, 2009
On the Geometry of Galaxies, Duke University Graduate/Faculty Seminar (Broad Audience Talk), October 16, 2009
An Overview of General Relativity (Broad Audience Talk), Duke University, October 3, 2008
An Overview of General Relativity, Wake Forest University, September 17, 2008
Negative Point Mass Singularites, Niels Bohr International Academy, April 11, 2008
On the Penrose Conjecture for Arbitrary Slices of a Spacetime, Niels Bohr International Academy, April 8, 2008
An Introduction to the Geometry of Black Holes, Niels Bohr International Academy, April 7, 2008
P.D.E.s Which Imply the Penrose Conjecture, Columbia University, October 4, 2007
What Do Black Holes and Soap Bubbles Have in Common? (Broad Audience Talk), Duke University, September 21, 2007
The Mass of Negative Point Mass Singularities in General Relativity (Conference on Global Differential Geometry), Muenster, Germany, August, 2006
Negative Point Mass Singularities in General Relativity, Rice University, November 16, 2005
Negative Point Mass Singularities in General Relativity, Michigan State University, November 08, 2005
Black Holes and the Curvature of Spacetime (Broad Audience Talk), Michigan State University, November 7, 2005
Negative Point Mass Singularities in General Relativity, Duke University, November 2, 2005
Negative Point Mass Singularities in General Relativity, Stanford University, September 21, 2005
Negative Point Mass Singularities in General Relativity, Sir Isaac Newton Institute, Cambridge, England (Research Talk), August, 2005
Generalization of the Hawking Mass, International Congress of Mathematical Physics, Lisbon, Portugal, August, 2003
Penrose Inequalities, Program on Penrose Inequalities at Erwin Schroedinger Institute, Vienna, Austria, July, 2003
Quasi-local Mass Functionals in General Relativity, Perspectives in Differential Geometry conference at BIRS, Banff, Canada, July, 2003
The Yamabe Invariants of 3-Manifolds, Great Lakes Geometry Conference (Calabi's 80th birthday), University of Wisconsin, Madison, May, 2003
Classification of Prime 3-Manifolds with Yamabe Invariant Greater than RP^3, First Yamabe Memorial Symposium, University of Minnesota, September, 2002
Black Holes, the Penrose Conjecture, and Quasi-local Mass, 50 Years of the Cauchy Problem in General Relativity, Cargese, Corsica (Research Talk), August, 2002
Classification of Prime 3-Manifolds with Yamabe Invariant Greater than RP^3, Differential Geometry Satellite Conference for the ICM, Tianjin, China, August, 2002
Generalization of the Hawking Mass, 50 Years of the Cauchy Problem in General Relativity, Cargese, Corsica (Research Talk), August, 2002
Proof of the Poincare Conjecture for 3-Manifolds with Yamabe Invariant Greater than RP^3, 50 Years of the Cauchy Problem in General Relativity, Cargese, Corsica (Research Talk), August, 2002
Proof of the Poincare Conjecture for 3-Manifolds with Yamabe Invariant Greater than RP^3 (Research Talk), Cargese, Corsica, France, 1 August 2002
The Riemannian Penrose Inequality, International Congress of Mathematicians, Beijing, China, August, 2002
On the Mass of Higher Dimensional Black Holes, 9th Annual Southern California Geometric Analysis Seminar, UC Irvine, February, 2002
Black Holes, Minimal Surfaces, and Geometric Flows, Duke Math Journal Conference, Duke University (Research Talk), April 28, 2001
Quasi-local Mass and Black Holes in General Relativity, Geometry Seminar, Duke University (Research Talk), April 28, 2001
Proof of the Riemannian Penrose Inequality Using the Positive Mass Theorem, Current Developments in Mathematics Conference, Harvard University, November, 1999
Proof of the Riemannian Penrose Conjecture, Institute for Theoretical Physics, UC Santa Barbara (Research Talk), June 25, 1999
On Dark Matter, Galaxies, and the Large Scale Geometry of the Universe, Duke University Graduate / Faculty Seminar (Research Talk, video available, slides the same as the above talk) - Talk begins at 5:20 of, February 15, 2013
Doctoral Theses Directed
Andrew Goetz, The Einstein-Klein-Gordon Equations, Wave Dark Matter, and the Tully-Fisher Relation, (2015)
Hangjun Xu, Uniformly Area Expanding Flows in Spacetimes, (2014)
Alan R. Parry, Wave Dark Matter and Dwarf Spheroidal Galaxies, (2013)
M. George Lam, The Graph Cases of the Riemannian Positive Mass and Penrose Inequalities in All Dimensions, (2011)
Graham H. Cox, Scalar Curvature Rigidity Theorems for the Upper Hemisphere, (2011)
Jeffrey Jauregui, Mass Estimates, Conformal Techniques, and Singularities in General Relativity, (2010)
Nicholas Robbins, Negative Point Mass Singularities in General Relativity, (2007)
Henri Roesch, Proof of a Null Penrose Conjecture Using a New Quasi-local Mass, (2017)
Publications
Papers Published
Bray, H; Hamm, B; Hirsch, S; Wheeler, J; Zhang, Y, Flatly foliated relativity,
Pure and Applied Mathematics Quarterly, vol. 15 no. 2
(January, 2019),
pp. 707-747, International Press of Boston
Bray, HL; Minicozzi, WP, The mathematics of richard schoen,
Notices of the American Mathematical Society, vol. 65 no. 12
(December, 2018),
pp. 1349-1176, American Mathematical Society (AMS)
Bray, HL; Minicozzi, WP, Preface,
Notices of the American Mathematical Society, vol. 65 no. 11
(December, 2018),
pp. 1412-1413
Bray, H; Roesch, H, Proof of a Null Geometry Penrose Conjecture,
Notices of the American Mathematical Society., vol. 65
(February, 2018), American Mathematical Society
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
(June, 2016),
pp. 1457-1475, Springer Nature, ISSN 1424-0637
Martinez-Medina, LA; Bray, H; Mattos, T, On wave dark matter in spiral and barred galaxies, vol. 2015 no. 12
(December, 2015),
pp. 025-025, IOP Publishing
Bray, HL; Jauregui, JL, On curves with nonnegative torsion,
Archiv Der Mathematik, vol. 104 no. 6
(June, 2015),
pp. 561-575, Springer Nature, ISSN 0003-889X
Bray, HL; Jauregui, JL, Time Flat Surfaces and the Monotonicity of the Spacetime Hawking Mass,
Communications in Mathematical Physics, vol. 335 no. 1
(April, 2015),
pp. 285-307, Springer Nature, ISSN 0010-3616
Bray, HL; Parry, AR, Modeling wave dark matter in dwarf spheroidal galaxies,
Journal of Physics: Conference Series, vol. 615
(2015),
pp. 012001-012001, IOP Publishing, ISSN 1742-6588
Bray, H; Goetz, AS, Wave Dark Matter and the Tully-Fisher Relation
(September, 2014)
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
Bray, HL; Jauregui, JL, A geometric theory of zero area singularities in general relativity,
Asian Journal of Mathematics, vol. 17 no. 3
(2013),
pp. 525-560, International Press of Boston, ISSN 1093-6106
Bray, H, On Wave Dark Matter, Shells in Elliptical Galaxies, and the Axioms of General Relativity
(December, 2012)
Bray, HL; Khuri, MA, P.D.E.'s Which Imply the Penrose Conjecture,
Asian Journal of Mathematics, vol. 15 no. 4
(December, 2011),
pp. 54, International Press
Bray, HL; Khuri, MA, P. D. E. 'S which imply the penrose conjecture,
Asian Journal of Mathematics, vol. 15 no. 4
(January, 2011),
pp. 557-610, International Press of Boston, ISSN 1093-6106
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
Bray, H; Brendle, S; Eichmair, M; Neves, A, Area-Minimizing Projective Planes in 3-Manifolds,
Communications on Pure and Applied Mathematics, vol. 63 no. 9
(September, 2010),
pp. 1237-1247, WILEY, ISSN 0010-3640
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. 741-766, American Institute of Mathematical Sciences (AIMS), ISSN 1078-0947
Bray, H; Brendle, S; Neves, A, Rigidity of area-minimizing two-spheres in three-manifolds,
Communications in Analysis and Geometry, vol. 18 no. 4
(January, 2010),
pp. 821-830, International Press of Boston, ISSN 1019-8385
Bray, HL; Lee, DA, On the Riemannian Penrose inequality in dimensions less than eight,
Duke Mathematical Journal, vol. 148 no. 1
(May, 2009),
pp. 81-106, Duke University Press, ISSN 0012-7094
Bray, H; Miao, P, On the capacity of surfaces in manifolds with nonnegative scalar curvature,
Inventiones Mathematicae, vol. 172 no. 3
(June, 2008),
pp. 459-475, Springer Nature, ISSN 0020-9910
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. 119-138, Springer Nature, ISSN 0010-3616
Bray, H, A Family of Quasi-local Mass Functionals with Monotone Flows, edited by Zambrini, JC,
Proceedings of the 14th International Congress on Mathematical Physics
(January, 2006),
pp. 323-329, World Scientific, ISBN 981256201X
H.L. Bray, The Positve Energy Theorem and Other Inequalities in GR,
in The Encyclopedia of Mathematical Physics
(2005)
Bray, H, The Positve Energy Theorem and Other Inequalities,
in The Encyclopedia of Mathematical Physics
(2005)
Bray, HL; Neves, A, Classification of Prime 3-Manifolds with Yamabe Invariant Greater than RP^3,
Annals of Mathematics, vol. 159 no. 1
(January, 2004),
pp. 407-424, Annals of Mathematics, Princeton U
Bray, H, Geometric Flows and the Penrose Inequality,
in Encyclopedia of Mathematical Physics: Five-Volume Set
(January, 2004),
pp. 510-520, ISBN 9780125126663
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
H.L. Bray, A Family of Quasi-local Mass Functionals with Monotone Flows,
in Proceedings of the 14th International Congress on Mathematical Physics, Lisbon, Portugal, 2003, edited by Jean-Claude Zambrini
(2003)
Bray, H; Morgan, F, An isoperimetric comparison theorem for schwarzschild space and other manifolds,
Proceedings of the American Mathematical Society, vol. 130 no. 5
(January, 2002),
pp. 1467-1472
Bray, H; Finster, F, Curvature estimates and the Positive Mass Theorem,
Communications in Analysis and Geometry, vol. 10 no. 2
(January, 2002),
pp. 291-306, International Press of Boston
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. 257-272
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. 1372-1381
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. 999-1016, International Press of Boston
Bray, HL, Proof of the riemannian penrose inequality using the positive mass theorem,
Journal of Differential Geometry, vol. 59 no. 2
(January, 2001),
pp. 177-267, International Press of Boston
Bray, H; Schoen, RM, Recent Proofs of the Riemannian Penrose Conjecture,
in Current Developments in Mathematics
(1999),
pp. 1-36, International Press
Bray, H; McCormick, K; Wells, RO; Zhou, XD, Wavelet variations on the Shannon sampling theorem.,
Biosystems, vol. 34 no. 1-3
(January, 1995),
pp. 249-257, Elsevier Science Ireland, ISSN 0303-2647
Other
Bray, H, The Penrose Inequality in General Relativity and Volume Comparison Theorems Involving Scalar Curvature
(1997) (thesis, Stanford University.)