Hubert L. Bray, Professor of Mathematics and Physics
Professor Bray studies geometric analysis, general relativity, and theoretical astrophysics. His interests include black holes, dark matter, and the curvature of spacetime.
Geometric analysis is the mathematics of curved spaces, like the surface of an apple, but from the point of view of an ant walking on the apple.
General relativity says that WE are the ant in a four dimensional spacetime. Gravity is explained by Einstein's "happiest thought," that matter curves spacetime.
However, most of the curvature of spacetime in galaxies is currently unexplained. Physicists refer to this largescale unexplained curvature as dark matter, which is one of the biggest mysteries in astrophysics today.
Video links for many of Professor Bray's talks are listed below under "Selected Invited Lectures." The videos labeled "Broad Audience Talk" are ideal for those with a general knowledge of math and physics. The "Research Talk" lectures are ideal for advanced graduate students and others working in these areas.  Contact Info:
Teaching (Fall 2014):
Teaching (Spring 2015):
 MATH 421.01, DIFFERENTIAL GEOMETRY
Synopsis
 Physics 047, TuTh 11:45 AM01:00 PM
 Office Hours:
 Mondays and Wednesdays, 4:30  5:30pm, and by appointment.
 Education:
PhD  Stanford University (adviser: Richard Schoen)  1997 
BA, BS,  Rice University, Math and Physics, summa cum laude  1992 
 Specialties:

Geometry
Analysis Mathematical Physics
 Research Interests: Geometric Analysis, General Relativity, Theoretical Astrophysics
 Curriculum Vitae
 Current Ph.D. Students
(Former Students)
 Postdocs Mentored
 Representative Publications
 H.L. Bray and A.S. Goetz, Wave Dark Matter and the TullyFisher Relation
(Preprint, September, 2014) [arXiv:1409.7347], [7347]
 H.L. Bray, J. L. Jauregui, M. Mars, Time Flat Surfaces and the Monotonicity of the Spacetime Hawking Mass II
(Preprint, February, 2014) [arXiv:1402.3287 [math.DG]], [3287] [abs]
 H.L. Bray and J. L. Jauregui, Time Flat Surfaces and the Monotonicity of the Spacetime Hawking Mass,
Communications in Mathematical Physics
(Accepted, April, 2014) [arXiv:1310.8638 [math.DG]], [8638]
 H.L. Bray and J. L. Jauregui, On Curves with Nonnegative Torsion
(Preprint, December, 2013) [arXiv:1312.5171 [math.DG]], [5171]
 H.L. Bray and A. R. Parry, Modeling Wave Dark Matter in Dwarf Spheroidal Galaxies
(Preprint, January, 2013) [html]
 H.L. Bray, On Wave Dark Matter, Shells in Elliptical Galaxies, and the Axioms of General Relativity
(Preprint, December 22, 2012) [html]
 H.L. Bray, On Dark Matter, Spiral Galaxies, and the Axioms of General Relativity,
AMS Contemporary Mathematics Volume, "Geometric Analysis, Mathematical Relativity, and Nonlinear Partial Differential Equations", vol. 599
(2013), American Mathematical Society [html]
 H.L. Bray, 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 Hubert L. Bray and William P. Minicozzi
(2011), Higher Education Press and International Press, Beijing and Boston [arXiv:1101.2230v1], [pdf] [author's comments]
 H.L. Bray and M.A. Khuri, P.D.E.'s Which Imply the Penrose Conjecture,
Asian Journal of Mathematics, vol. 15 no. 4
(December, 2011),
pp. 54, International Press, ISSN 10936106 [pdf] [author's comments]
 H.L. Bray and M.A. Khuri, A Jang Equation Approach to the Penrose Inequality,
Discrete and Continuous Dynamical Systems A, vol. 27 no. 2
(June, 2010) [arXiv:0910.4785v1]
 H.L. Bray, S. Brendle, M. Eichmair, A. Neves, AreaMinimizing Projective Planes in 3Manifolds,
Communications in Pure and Applied Mathematics
(2010) [arXiv:0909.1665v1]
 H.L. Bray, S. Brendle, A. Neves, Rigidity of AreaMinimizing TwoSpheres in ThreeManifolds,
Communications in Analysis and Geometry
(2010) [arXiv:1002.2814]
 H.L. Bray and J.L. Jauregui, A Geometric Theory of Zero Area Singularities in General Relativity,
Asian Journal of Mathematics, vol. 17 no. 3
(September, 2013),
pp. 525560 [arXiv:0909.0522v1]
 H.L. Bray, D.A. Lee, On the Riemannian Penrose Inequality in Dimension Less Than Eight,
Duke Mathematical Journal, vol. 148 no. 1
(2009),
pp. 81106 [arXiv:0705.1128v1], [pdf]
 H.L. Bray, P. Miao, On the Capacity of Surfaces in Manifolds with Nonnegative Scalar Curvature,
Inventiones Mathematicae, vol. 172 no. 3
(June, 2008) [arXiv:0707.3337v1]
 H.L. Bray, S. Hayward, M. Mars, W. Simon, Generalized Inverse Mean Curvature Flows in Spacetime,
Communications in Mathematical Physics, vol. 272 no. 1
(May, 2007),
pp. 119138 [arXiv:grqc/0603014v1]
 H.L. Bray and A. Neves, Classification of Prime 3Manifolds with Yamabe Invariant Greater than RP^3,
Annals of Mathematics, vol. 159 no. 1
(2004),
pp. 407424 [p09]
 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]
 H. L. Bray and F. Finster, Curvature Estimates and the Positive Mass Theorem,
Communications in Analysis and Geometry, vol. 10 no. 2
(2002),
pp. 291306 [arXiv:math/9906047v3]
 H.L. Bray and K. Iga, Superharmonic Functions in R^n and the Penrose Inequality in General Relativity,
Communications in Analysis and Geometry, vol. 10 no. 5
(2002),
pp. 9991016
 H. L. Bray and F. Morgan, An Isoperimetric Comparison Theorem for Schwarzschild Space and Other Manifolds,
Proceedings of the American Mathematical Society, vol. 130 no. 5
(2002),
pp. 14671472 [pdf]
 H. L. Bray, Proof of the Riemannian Penrose Inequality Using the Positive Mass Theorem,
Journal of Differential Geometry, vol. 59 no. 2
(2001),
pp. 177267 [arXiv:math/9911173v1], [pdf]
 H. L. Bray and R.M. Schoen, Recent Proofs of the Riemannian Penrose Conjecture,
in Current Developments in Mathematics, 1999 (Cambridge, MA)
(1999),
pp. 136, Int. Press, Somerville, MA
 H.L. Bray, The Positve Energy Theorem and Other Inequalities in GR,
in The Encyclopedia of Mathematical Physics
(2005)
 H.L. Bray and P.T. Chrusciel, 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 P.T. Chrusciel and H.F. Friedrich
(2004), Birkhauser [arXiv:grqc/0312047v2]
 H.L. Bray, Black Holes, Geometric Flows, and the Penrose Inequality in General Relativity,
Notices of the American Mathematical Society, vol. 49 no. 11
(2002),
pp. 13721381
 H.L. Bray, Black Holes and the Penrose Inequality in General Relativity,
in Proceedings of the International Congress of Mathematicians, Beijing, China, 2002, vol. 2
(2002),
pp. 257272 [arXiv:math/0304261v1]
 H.L. Bray, K. McCormick, R.O. Wells, Jr., Xiaodong Zhou, Wavelet Variations on the Shannon Sampling Theorem,
Biosystems, vol. 34
(1995),
pp. 249257, Elsevier Science Ireland [science] [author's comments]
 H.L. Bray, The Penrose Inequality in General Relativity and Volume Comparison Theorems Involving Scalar Curvature
(1997) (thesis, Stanford University.) [arXiv:0902.3241v1]
 Selected Invited Lectures
 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, December 6, 2010, Duke University (Survey Talk) 112 minutes total  Part I (66 minutes): Bray describes the astronomical evidence for dark matter in galaxies. Part II (21 minutes, 66 minutes in): Badin describes searches for dark matter particles. Part III (25 minutes, 87 minutes in): Bray describes his work on a general relativity approach to dark matter described by a scalar field satisfying the KleinGordon equation as a possible explanation for spiral patterns in galaxies [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, December 13, 2010, University of Tennessee (Broad Audience Talk) 45 minutes [video.html]
 From Pythagoras to Einstein: How Geometry Describes the LargeScale Structure of the Universe (Part 1), March 26, 2011, Duke University Graduate Student Recruiting Weekend (Broad Audience Talk) [video.html]
 From Pythagoras to Einstein: How Geometry Describes the LargeScale Structure of the Universe (Part 2), March 26, 2011, Duke University Graduate Student Recruiting Weekend (Broad Audience Talk) [video.html]
 An Overview of General Relativity, October 3, 2008, Duke University Graduate/Faculty Seminar (Broad Audience Talk) [video.html]
 What Do Black Holes and Soap Bubbles Have in Common?, September 21, 2007, Duke University Graduate/Faculty Seminar (Broad Audience Talk) [video.html]
 Black Holes and the Curvature of Spacetime, November 7, 2005, Michigan State University (Broad Audience Talk) [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
 2014  2017 Time Flat Curves and Surfaces, Geometric Flows, and the Penrose Conjecture, National Science Foundation, DMS1406396.
 2010  2013: Scalar Curvature, the Penrose Conjecture, and the Axioms of General Relativity (extended through 2014), National Science Foundation, DMS1007063.
 2007  2010: 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
 Park City Mathematics Institute Summer Program on Geometric Analysis, Organizer (with Greg Galloway, Rafe Mazzeo, and Natasa Sesum), July, 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 held at Duke University, 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
