**Office Location:** 189 Physics Bldg, Durham, NC 27710**Office Phone:** (617) 596-7273, (919) 757-8428**Email Address:** hubert.bray@duke.edu**Web Page:** http://www.math.duke.edu/~bray/main.html

**Specialties:**

Geometry

Analysis

Mathematical Physics

**Education:**

Ph.D., Stanford University, 1997

B.A., Rice University, 1992

**Research Categories:** *Geometric Analysis, General Relativity, Theoretical Astrophysics*

**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

**Representative Publications**

- 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, Accepted, 2015), pp. 025-025 [arXiv:1505.07154], [1505.07154], [doi] . - Bray, H; Goetz, AS,
*Wave Dark Matter and the Tully-Fisher Relation*(Preprint, September, 2014) [arXiv:1409.7347], [7347] [abs]. - 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 (July 26, 2015), pp. 1457-1475, Springer Basel [arXiv:1402.3287 [math.DG]], [3287], [doi] [abs]. - Bray, HL; Jauregui, JL,
*Time Flat Surfaces and the Monotonicity of the Spacetime Hawking Mass*, Communications in Mathematical Physics, vol. 335 no. 1 (April, 2014), pp. 285-307 [arXiv:1310.8638 [math.DG]], [8638], [doi] . - Bray, HL; Jauregui, JL,
*On curves with nonnegative torsion*, Archiv der Mathematik, vol. 104 no. 6 (2015), pp. 561-575 [arXiv:1312.5171 [math.DG]], [c8d239381b86496b96d95ff26f1061eb], [doi] . - Bray, HL; Parry, AR,
*Modeling wave dark matter in dwarf spheroidal galaxies*, Journal of Physics, vol. 615 (2015) [Gateway.cgi], [doi] . - Bray, H,
*On Wave Dark Matter, Shells in Elliptical Galaxies, and the Axioms of General Relativity*(Preprint, December 22, 2012) [pdf] [abs]. - 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 [arXiv:1004.4016], [html] . - 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 [arXiv:1101.2230v1], [2230] [author's comments]. - Bray, HL; Khuri, MA,
*P. D. E. 'S which imply the penrose conjecture*, Asian Journal of Mathematics, vol. 15 no. 4 (December, 2011), pp. 557-610, International Press [pdf] [abs] [author's comments]. - Bray, HL; Khuri, MA,
*A jang equation approach to the penrose inequality*, Discrete and Continuous Dynamical Systems, vol. 27 no. 2 (June, 2010), pp. 741-766 [arXiv:0910.4785v1], [doi] [abs]. - 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 [arXiv:0909.1665v1], [doi] [abs]. - 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 [arXiv:1002.2814] [abs]. - Bray, HL; Jauregui, JL,
*A geometric theory of zero area singularities in general relativity*, Asian Journal of Mathematics, vol. 17 no. 3 (September, 2013), pp. 525-560 [arXiv:0909.0522v1], [doi] [abs]. - 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 [arXiv:0705.1128v1], [pdf], [doi] [abs]. - 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 [arXiv:0707.3337v1], [doi] [abs]. - 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 [arXiv:gr-qc/0603014v1], [doi] [abs]. - 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 [p09] [abs]. - Bray, H,
*The Positve Energy Theorem and Other Inequalities*, in The Encyclopedia of Mathematical Physics (2005) . - 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] . - Bray, H; Finster, F,
*Curvature estimates and the Positive Mass Theorem*, Communications in Analysis and Geometry, vol. 10 no. 2 (2002), pp. 291-306 [arXiv:math/9906047v3] [abs]. - 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, 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 [pdf], [doi] [abs]. - 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 [arXiv:math/9911173v1], [pdf] [abs]. - Bray, H; Schoen, RM,
*Recent Proofs of the Riemannian Penrose Conjecture*, in Current Developments in Mathematics (1999), pp. 1-36, International Press . - H.L. Bray,
*The Positve Energy Theorem and Other Inequalities in GR*, in The Encyclopedia of Mathematical Physics (2005) . - 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 [arXiv:gr-qc/0312047v2] . - 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 [pdf] . - 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 [arXiv:math/0304261v1], [0304261v1] . - 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 [science], [doi] [abs] [author's comments]. - Bray, H,
*The Penrose Inequality in General Relativity and Volume Comparison Theorems Involving Scalar Curvature*(1997) (thesis, Stanford University.) [arXiv:0902.3241v1] .

**Current Ph.D. Students**(Former Students)

**Postdocs Mentored**- Carla Cederbaum (July, 2011 - January, 2013)
- Ye Li (2009 - 2011)
- Dan Lee (2005 - 2008)
- Fernando Schwartz (2005 - 2008)

**Selected Invited Lectures***The Geometry of the Universe (Research Lecture) : University of Waterloo*, March 09, 2015, University of Waterloo*Two lectures on the geometry of space and time (General audience talks)*, March 09, 2015, University of Waterloo [pdf]*From Pythagoras to Einstein: The Geometry of Space and Time (General audience talk)*, March 09, 2015, University of Waterloo [watch]*The Science behind "Trevor the Time Traveler” (For everyone, ages 8 and up)*, March 09, 2015, University of Waterloo [watch]*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, UC-San 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 (Survey Talk)*, December 6, 2010, Duke University [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 (Broad Audience Talk) : 45 minutes*, December 13, 2010, University of Tennessee*From Pythagoras to Einstein: How Geometry Describes the Large-Scale Structure of the Universe (Part 1) (Broad Audience Talk)*, March 26, 2011, Duke University*From Pythagoras to Einstein: How Geometry Describes the Large-Scale Structure of the Universe (Part 2) (Broad Audience Talk)*, March 26, 2011, Duke University*An Overview of General Relativity (Broad Audience Talk)*, October 3, 2008, Duke University*What Do Black Holes and Soap Bubbles Have in Common? (Broad Audience Talk)*, September 21, 2007, Duke University [video.html]*Black Holes and the Curvature of Spacetime (Broad Audience Talk)*, November 7, 2005, Michigan State University [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 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]*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]*Black Holes, Minimal Surfaces, and Geometric Flows*, April 28, 2001, Duke Math Journal Conference, Duke University (Research Talk) [video.html]*Quasi-local 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]