Box 90320, Durham, NC 27708-0320 (617) 596-7273, (919) 757-8428

Ph.D. Stanford University 1997 B.A. Rice University 1992

Geometric Analysis, General Relativity, Theoretical Astrophysics

- 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

- 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
- 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

- Andrew Goetz, (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)

- Papers Published

- 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 Basel .- Bray, HL; Jauregui, JL,
On curves with nonnegative torsion, Archiv der Mathematik, vol. 104 no. 6 (June, 2015), pp. 561-575 .- 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 .- Bray, HL; Parry, AR,
Modeling wave dark matter in dwarf spheroidal galaxies, Journal of Physics, vol. 615 (2015) .- 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 .- 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 .- Bray, HL; Khuri, MA,
P. D. E. 'S which imply the penrose conjecture, Asian Journal of Mathematics, vol. 15 no. 4 (2011), pp. 557-610, International Press .- Bray, H; Brendle, S; Neves, A,
Rigidity of area-minimizing two-spheres in three-manifolds, Communications in Analysis and Geometry, vol. 18 no. 4 (2010), pp. 821-830 .- Bray, H; Brendle, S; Eichmair, M; Neves, A,
Area-Minimizing Projective Planes in 3-Manifolds, Communications on Pure & Applied Mathematics, vol. 63 no. 9 (2010), pp. 1237-1247 .- Bray, HL; Khuri, MA,
A jang equation approach to the penrose inequality, Discrete and Continuous Dynamical Systems, vol. 27 no. 2 (2010), pp. 741-766 .- Bray, HL; Lee, DA,
On the Riemannian Penrose inequality in dimensions less than eight, Duke Mathematical Journal, vol. 148 no. 1 (2009), pp. 81-106 .- Bray, H; Miao, P,
On the capacity of surfaces in manifolds with nonnegative scalar curvature, Inventiones mathematicae, vol. 172 no. 3 (2008), pp. 459-475 .- Bray, H; Hayward, S; Mars, M; Simon, W,
Generalized inverse mean curvature flows in spacetime, Communications in Mathematical Physics, vol. 272 no. 1 (2007), pp. 119-138 .- Bray, HL,
A family of quasi-local mass functionals with monotone flows, edited by JC Zambrini (January, 2006), pp. 323-329 .- 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 .- 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,
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, 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. 1467-1472 .- Bray, H; Finster, F,
Curvature estimates and the Positive Mass Theorem, Communications in Analysis and Geometry, vol. 10 no. 2 (2002), pp. 291-306 .- 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 .- Bray, HL,
Proof of the Riemannian Penrose inequality using the positive mass theorem, Journal of Differential Geometry, vol. 59 no. 2 (2001), pp. 177-267 .- 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; Jr, ROW; Zhou, X-D,
Wavelet variations on the Shannon sampling theorem, BioSystems, vol. 34 no. 1-3 (1995), pp. 249-257, Elsevier Science Ireland .- Papers Accepted

- Martinez-Medina, 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, 2015), pp. 025-025 .- Preprints

- Bray, H; Goetz, AS,
Wave Dark Matter and the Tully-Fisher Relation(September, 2014) .- Bray, H,
On Wave Dark Matter, Shells in Elliptical Galaxies, and the Axioms of General Relativity(December, 2012) .- Other

- Bray, H,
The Penrose Inequality in General Relativity and Volume Comparison Theorems Involving Scalar Curvature(1997)(thesis, Stanford University.) .

Last modified: 2017/12/16