Math @ Duke

Hubert L. Bray, Professor of Mathematics and Physics
Professor Hubert Bray studies geometric analysis with applications to general relativity and the largescale geometry of spacetimes. He is a member of the mathematics and physics departments at Duke University.
Video links for many of his 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 (Spring 2014):
 MATH 421.01, DIFFERENTIAL GEOMETRY
Synopsis
 Physics 235, TuTh 11:45 AM01:00 PM
 MATH 79090.06, MINICOURSE IN ADVANCED TOPICS
Synopsis
 Physics 227, MWF 10:20 AM11:10 AM
Teaching (Fall 2014):
 MATH 89S.01, FIRSTYEAR SEMINAR (TOP)
Synopsis
 Physics 227, MW 01:25 PM02:40 PM
 MATH 333.01, COMPLEX ANALYSIS
Synopsis
 Physics 227, MW 03:05 PM04:20 PM
 Office Hours:
 4:30 to 6:30 on Wednesdays, or by appointment. Please email me if you are coming after 5pm so that I know not to leave early.
 Education:
PhD  Stanford University (adviser: Richard Schoen)  1997 
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, 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 Elliptical 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]
 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
 2010  2013: Scalar Curvature, the Penrose Conjecture, and the Axioms of General Relativity, 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


dept@math.duke.edu
ph: 919.660.2800
fax: 919.660.2821
 
Mathematics Department
Duke University, Box 90320
Durham, NC 277080320

