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Hubert Bray, Professor of Mathematics and Physics

Hubert Bray

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 large-scale unexplained curvature as dark matter, which is one of the biggest mysteries in astrophysics today. For ages 8 and up, watch Professor Bray talk about his science fiction book "Trevor the Time Traveler" at https://www.youtube.com/watch?v=LNogSQVcNzQ.

Contact Info:
Office Location:  189
Office Phone:  (617) 596-7273, (919) 757-8428
Email Address: send me a message
Web Page:  http://www.math.duke.edu/~bray/main.html

Teaching (Spring 2016):

  • MATH 89S.02, FIRST-YEAR SEMINAR (TOP) Synopsis
    Physics 205, MW 03:05 PM-04:20 PM
  • MATH 421.01, DIFFERENTIAL GEOMETRY Synopsis
    Physics 259, MW 01:25 PM-02:40 PM
  • MATH 790-90.02, MINICOURSE IN ADVANCED TOPICS Synopsis
    Physics 227, MWF 10:20 AM-11:10 AM
Teaching (Fall 2016):

  • MATH 89S.01, FIRST-YEAR SEMINAR (TOP) Synopsis
    Physics 205, TuTh 10:05 AM-11:20 AM
  • MATH 690-20.01, DIFFERENTIAL GEOMETRY (TOP) Synopsis
    Physics 227, TuTh 11:45 AM-01:00 PM
Office Hours:

Mondays and Wednesdays, 4:30 - 5:30 p.m.
Education:

Ph.D.Stanford University1997
B.A.Rice University1992
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)

Postdocs Mentored

Representative Publications   (More Publications)

  1. LA Martinez-Medina, HL Bray and T Matos, On wave dark matter in spiral and barred galaxies, Journal of Cosmology and Astroparticle Physics, vol. 2015 no. 12 (December, Accepted, 2015), pp. 025-025 [arXiv:1505.07154], [1505.07154], [doi]
  2. H Bray and AS Goetz, Wave Dark Matter and the Tully-Fisher Relation, manual (Preprint, September, 2014) [arXiv:1409.7347], [7347]  [abs]
  3. HL Bray and JL Jauregui, Time Flat Surfaces and the Monotonicity of the Spacetime Hawking Mass, Communications in Mathematical Physics, vol. 335 no. 1 (April, 2014), pp. 285-307, ISSN 0010-3616 [arXiv:1310.8638 [math.DG]], [8638], [doi]
  4. HL Bray and JL Jauregui, On curves with nonnegative torsion, Archiv der Mathematik, vol. 104 no. 6 (2015), pp. 561-575, ISSN 0003-889X [arXiv:1312.5171 [math.DG]], [c8d239381b86496b96d95ff26f1061eb], [doi]
  5. HL Bray and AR Parry, Modeling wave dark matter in dwarf spheroidal galaxies, 9TH BIENNIAL CONFERENCE ON CLASSICAL AND QUANTUM RELATIVISTIC DYNAMICS OF PARTICLES AND FIELDS (IARD 2014), vol. 615 (2015), ISSN 1742-6588 [Gateway.cgi], [doi]
  6. H Bray, On Wave Dark Matter, Shells in Elliptical Galaxies, and the Axioms of General Relativity, manual (Preprint, December 22, 2012) [pdf]  [abs]
  7. HL Bray, 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]
  8. H 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 H Bray and W Minicozzi, manual (2011), Higher Education Press and International Press, Beijing and Boston [arXiv:1101.2230v1], [2230]  [author's comments]
  9. HL Bray and MA Khuri, P. D. E. 'S which imply the penrose conjecture, Asian Journal of Mathematics, vol. 15 no. 4 (December, 2011), pp. 557-610, International Press, ISSN 1093-6106 [pdf]  [abs] [author's comments]
  10. HL Bray and MA Khuri, A jang equation approach to the penrose inequality, Discrete and Continuous Dynamical Systems, vol. 27 no. 2 (June, 2010), pp. 741-766, ISSN 1078-0947 [arXiv:0910.4785v1], [doi]  [abs]
  11. H Bray, S Brendle, M Eichmair and A Neves, Area-Minimizing Projective Planes in 3-Manifolds, Communications on Pure and Applied Mathematics, vol. 63 no. 9 (2010), pp. 1237-1247, ISSN 0010-3640 [arXiv:0909.1665v1], [doi]  [abs]
  12. H Bray, S Brendle and A Neves, Rigidity of area-minimizing two-spheres in three-manifolds, Communications in Analysis and Geometry, vol. 18 no. 4 (2010), pp. 821-830, ISSN 1019-8385 [arXiv:1002.2814]  [abs]
  13. HL Bray and JL Jauregui, A geometric theory of zero area singularities in general relativity, Asian Journal of Mathematics, vol. 17 no. 3 (September, 2013), pp. 525-560, ISSN 1093-6106 [arXiv:0909.0522v1], [doi]  [abs]
  14. HL Bray and DA Lee, On the Riemannian Penrose inequality in dimensions less than eight, Duke Mathematical Journal, vol. 148 no. 1 (2009), pp. 81-106, ISSN 0012-7094 [arXiv:0705.1128v1], [pdf], [doi]  [abs]
  15. H Bray and P Miao, On the capacity of surfaces in manifolds with nonnegative scalar curvature, Inventiones Mathematicae, vol. 172 no. 3 (June, 2008), pp. 459-475, ISSN 0020-9910 [arXiv:0707.3337v1], [doi]  [abs]
  16. H Bray, S Hayward, M Mars and W Simon, Generalized inverse mean curvature flows in spacetime, Communications in Mathematical Physics, vol. 272 no. 1 (May, 2007), pp. 119-138, ISSN 0010-3616 [arXiv:gr-qc/0603014v1], [doi]  [abs]
  17. HL Bray and A Neves, Classification of Prime 3-Manifolds with Yamabe Invariant Greater than RP^3, Annals of Mathematics, vol. 159 no. 1 (January, 2004), pp. 407-424 [p09]  [abs]
  18. H Bray, The Positve Energy Theorem and Other Inequalities, in The Encyclopedia of Mathematical Physics, manual (2005)
  19. 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) [Family%20of%20Quasi-local%20Mass%20Functionals%20with%20Monotone%20Flows&f=false]
  20. H Bray and F Finster, Curvature estimates and the Positive Mass Theorem, Communications in Analysis and Geometry, vol. 10 no. 2 (2002), pp. 291-306 [arXiv:math/9906047v3]  [abs]
  21. HL 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. 999-1016
  22. H 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. 1467-1472 [pdf], [doi]  [abs]
  23. HL Bray, Proof of the Riemannian Penrose inequality using the positive mass theorem, Journal of Differential Geometry, vol. 59 no. 2 (2001), pp. 177-267 [arXiv:math/9911173v1], [pdf]  [abs]
  24. H Bray and RM Schoen, Recent Proofs of the Riemannian Penrose Conjecture, in Current Developments in Mathematics, manual (1999), pp. 1-36, International Press
  25. H.L. Bray, The Positve Energy Theorem and Other Inequalities in GR, in The Encyclopedia of Mathematical Physics (2005)
  26. H Bray and PT 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 PT Chrusciel and HF Friedrich, manual (2004), Birkhauser [arXiv:gr-qc/0312047v2]
  27. HL Bray, 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 [pdf]
  28. H Bray, 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 [arXiv:math/0304261v1], [0304261v1]
  29. H Bray, K McCormick, ROW Jr and X-D Zhou, Wavelet variations on the Shannon sampling theorem, BioSystems, vol. 34 no. 1-3 (1995), pp. 249-257, Elsevier Science Ireland, ISSN 0303-2647 [science], [doi]  [abs] [author's comments]
  30. H Bray, The Penrose Inequality in General Relativity and Volume Comparison Theorems Involving Scalar Curvature, manual (1997) (thesis, Stanford University.) [arXiv:0902.3241v1]
Selected Invited Lectures

  1. The Geometry of the Universe (Research Lecture) : University of Waterloo, March 09, 2015, University of Waterloo    
  2. Two lectures on the geometry of space and time (General audience talks), March 09, 2015, University of Waterloo [pdf]    
  3. From Pythagoras to Einstein: The Geometry of Space and Time (General audience talk), March 09, 2015, University of Waterloo [watch]    
  4. The Science behind "Trevor the Time Traveler” (For everyone, ages 8 and up), March 09, 2015, University of Waterloo [watch]    
  5. 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]    
  6. 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]    
  7. 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]    
  8. 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]    
  9. On the Monotonicity of the Hawking Mass for Time Flat Surfaces, October 11, 2013, New York General Relativity Seminar, Columbia University (Research Talk)    
  10. On Wave Dark Matter and the Geometry of Galaxies, May 24, 2013, JDG Conference, Lehigh University (Research Talk) [html]    
  11. On Dark Matter, Galaxies, and the Large Scale Geometry of the Universe, February 24, 2013, The 20th Southern California Geometric Analysis Seminar, UC-San Diego (Research Talk, slides only, but video of the similar talk below is available) [pdf]    
  12. 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]    
  13. 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]    
  14. Dark Matter in Galaxies (Dark Matter Awareness Week talk) by Hubert Bray and Andriy Badin (Survey Talk), December 6, 2010, Duke University [video.html]    
  15. 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    
  16. From Pythagoras to Einstein: How Geometry Describes the Large-Scale Structure of the Universe (Part 1) (Broad Audience Talk), March 26, 2011, Duke University    
  17. From Pythagoras to Einstein: How Geometry Describes the Large-Scale Structure of the Universe (Part 2) (Broad Audience Talk), March 26, 2011, Duke University    
  18. An Overview of General Relativity (Broad Audience Talk), October 3, 2008, Duke University    
  19. What Do Black Holes and Soap Bubbles Have in Common? (Broad Audience Talk), September 21, 2007, Duke University [video.html]    
  20. Black Holes and the Curvature of Spacetime (Broad Audience Talk), November 7, 2005, Michigan State University [html]    
  21. Negative Point Mass Singularities in General Relativity, August, 2005, Sir Isaac Newton Institute, Cambridge, England (Research Talk) [available here]    
  22. Generalization of the Hawking Mass, August, 2002, 50 Years of the Cauchy Problem in General Relativity, Cargese, Corsica (Research Talk) [available here]    
  23. Proof of the Poincare Conjecture for 3-Manifolds with Yamabe Invariant Greater than RP^3, August, 2002, 50 Years of the Cauchy Problem in General Relativity, Cargese, Corsica (Research Talk) [available here]    
  24. Black Holes, the Penrose Conjecture, and Quasi-local Mass, August, 2002, 50 Years of the Cauchy Problem in General Relativity, Cargese, Corsica (Research Talk) [available here]    
  25. Black Holes, Minimal Surfaces, and Geometric Flows, April 28, 2001, Duke Math Journal Conference, Duke University (Research Talk) [video.html]    
  26. Quasi-local Mass and Black Holes in General Relativity, April 28, 2001, Geometry Seminar, Duke University (Research Talk) [video.html]    
  27. 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, DMS-1406396.      
  • Scalar Curvature, the Penrose Conjecture, and the Axioms of General Relativity, National Science Foundation, DMS-1007063.      
  • Geometric Analysis Applied to General Relativity, National Science Foundation, DMS-0706794.      
  • 2002 - 2007: Scalar Curvature, Geometric Flows, and the General Penrose Conjecture, National Science Foundation, DMS-0533551 (DMS-0206483 before transfered to Duke).      
  • 1999 - 2002: A Continuing Investigation of the Penrose Conjecture in General Relativity, National Science Foundation, DMS-9971960.      
  • 1997 - 1999: Mathematical Sciences Postdoctoral Research Fellowship, National Science Foundation, DMS-9706006.      
Conferences Organized

 

dept@math.duke.edu
ph: 919.660.2800
fax: 919.660.2821

Mathematics Department
Duke University, Box 90320
Durham, NC 27708-0320