Hubert Bray
Professor of Mathematics
Professor Bray uses differential geometry to understand general relativity, and general relativity to motivate interesting problems in differential geometry. In 2001, he published his proof of the Riemannian Penrose Conjecture about the mass of black holes using geometric ideas related to minimal surfaces, scalar curvature, conformal geometry, geometric flows, and harmonic functions. He is also interested in the large-scale unexplained curvature of the universe, otherwise known as dark matter, which makes up most of the mass of galaxies. Professor Bray has proposed geometric explanations for dark matter which he calls "wave dark matter," which motivate very interesting questions about geometric partial differential equations.
Professor Bray has supervised 8 math Ph.D. graduates at Duke from 2006 to 2017. He is currently supervising one math Ph.D. student and one physics Ph.D. student. His most recent Ph.D. graduate, Henri Roesch, proved a Null Penrose Conjecture, open since 1973, as his thesis. While the physical motivation about the mass of black holes is the same as for the Riemannian Penrose Conjecture, the geometry involved is almost unrecognizably different, and may be viewed as a fundamental result about null geometry.
Professor Bray has supervised 8 math Ph.D. graduates at Duke from 2006 to 2017. He is currently supervising one math Ph.D. student and one physics Ph.D. student. His most recent Ph.D. graduate, Henri Roesch, proved a Null Penrose Conjecture, open since 1973, as his thesis. While the physical motivation about the mass of black holes is the same as for the Riemannian Penrose Conjecture, the geometry involved is almost unrecognizably different, and may be viewed as a fundamental result about null geometry.
Current Appointments & Affiliations
- Professor of Mathematics, Mathematics, Trinity College of Arts & Sciences 2004
Contact Information
- 189 Physics Bldg, Durham, NC 27710
- Box 90320, Durham, NC 27708-0320
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hubert.bray@duke.edu
(919) 757-8428
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Professor Bray's Main Webpage
- Background
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Education, Training, & Certifications
- Ph.D., Stanford University 1997
- B.A., Rice University 1992
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Previous Appointments & Affiliations
- Director of Undergraduate Studies in the Department of Mathematics, Mathematics, Trinity College of Arts & Sciences 2019 - 2022
- Professor of Physics, Physics, Trinity College of Arts & Sciences 2019 - 2022
- Professor in the Department of Physics, Physics, Trinity College of Arts & Sciences 2011 - 2019
- Recognition
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In the News
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JUL 3, 2014 Duke Today -
JUL 3, 2014 -
MAR 17, 2014
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Awards & Honors
- Community Service Award. Duke University’s Office of Durham and Regional Affairs. 2014
- Fellow of the AMS, Inaugural Class. The American Mathematical Society. January 2013
- Sloan Research Fellowship-Mathematics. Alfred P. Sloan Foundation. 2001
- 1997 - 1999: Mathematical Sciences Postdoctoral Research Fellowship. National Science Foundation. 1997
- Expertise
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Subject Headings
- Research
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Selected Grants
- Time Flat Curves and Surfaces, Geometric Flows, and the Penrose Conjecture awarded by National Science Foundation 2014 - 2018
- Scalar Curvature, the Penrose Conjecture, and the Axioms of General Relativity awarded by National Science Foundation 2010 - 2014
- Geometric Analysis Applied to General Relativity awarded by National Science Foundation 2007 - 2010
- Scalar Curvature, Geometric Flow, and the General Penrose Conjecture awarded by National Science Foundation 2005 - 2008
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External Relationships
- American Scholastic Convention
- Publications & Artistic Works
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Selected Publications
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Academic Articles
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Bray, Hubert, Daniel Stern, Marcus Khuri, and Demetre Kazaras. “Harmonic Functions and The Mass of 3-Dimensional Asymptotically Flat Riemannian Manifolds,” November 15, 2019.Link to Item
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Bray, Hubert, and Daniel Stern. “Scalar curvature and harmonic one-forms on three-manifolds with boundary,” November 15, 2019.Link to Item
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Bray, Hubert, Zhenhua Liu, Yiyue Zhang, and Feng Gui. “Proof of Bishop's volume comparison theorem using singular soap bubbles,” March 29, 2019.Link to Item
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Bray, H., B. Hamm, S. Hirsch, J. Wheeler, and Y. Zhang. “Flatly foliated relativity.” Pure and Applied Mathematics Quarterly 15, no. 2 (January 1, 2019): 707–47. https://doi.org/10.4310/PAMQ.2019.v15.n2.a4.Full Text
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Bray, H. L., and W. P. Minicozzi. “Preface.” Notices of the American Mathematical Society 65, no. 11 (December 1, 2018): 1412–13. https://doi.org/10.1090/noti1748.Full Text
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Bray, H. L., and W. P. Minicozzi. “The mathematics of richard schoen.” Notices of the American Mathematical Society 65, no. 12 (December 1, 2018): 1349–1176. https://doi.org/10.1090/NOTI1749.Full Text
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Bray, H., and H. Roesch. “Proof of a Null Geometry Penrose Conjecture.” Notices of the American Mathematical Society. 65 (February 1, 2018).
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Bray, H. L., J. L. Jauregui, and M. Mars. “Time Flat Surfaces and the Monotonicity of the Spacetime Hawking Mass II.” Annales Henri Poincare 17, no. 6 (June 1, 2016): 1457–75. https://doi.org/10.1007/s00023-015-0420-2.Full Text
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Bray, H. L., and J. L. Jauregui. “On curves with nonnegative torsion.” Archiv Der Mathematik 104, no. 6 (June 29, 2015): 561–75. https://doi.org/10.1007/s00013-015-0767-0.Full Text
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Bray, H. L., and J. L. Jauregui. “Time Flat Surfaces and the Monotonicity of the Spacetime Hawking Mass.” Communications in Mathematical Physics 335, no. 1 (April 1, 2015): 285–307. https://doi.org/10.1007/s00220-014-2162-2.Full Text
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Bray, H., and A. S. Goetz. “Wave Dark Matter and the Tully-Fisher Relation,” September 2014.Link to Item
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Bray, H. L. “On Dark Matter, Spiral Galaxies, and the Axioms of General Relativity (Accepted).” Ams Contemporary Mathematics Volume 599, no. Geometric Analysis, Mathematical Relativity, and Nonlinear Partial Differential Equations (2013).Link to Item
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Bray, H. L., and J. L. Jauregui. “A geometric theory of zero area singularities in general relativity.” Asian Journal of Mathematics 17, no. 3 (2013): 525–60. https://doi.org/10.4310/AJM.2013.v17.n3.a6.Full Text
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Bray, H. “On Wave Dark Matter, Shells in Elliptical Galaxies, and the Axioms of General Relativity,” December 22, 2012.Link to Item
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Bray, H. L., and M. A. Khuri. “P.D.E.'s Which Imply the Penrose Conjecture.” Asian Journal of Mathematics 15, no. 4 (December 2011): 54.Link to Item
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Bray, H. L., and M. A. Khuri. “P. D. E. 'S which imply the penrose conjecture.” Asian Journal of Mathematics 15, no. 4 (January 1, 2011): 557–610. https://doi.org/10.4310/AJM.2011.v15.n4.a5.Full Text
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Bray, H., S. Brendle, M. Eichmair, and A. Neves. “Area-Minimizing Projective Planes in 3-Manifolds.” Communications on Pure and Applied Mathematics 63, no. 9 (September 1, 2010): 1237–47. https://doi.org/10.1002/cpa.20319.Full Text
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Bray, H. L., and M. A. Khuri. “A jang equation approach to the penrose inequality.” Discrete and Continuous Dynamical Systems 27, no. 2 (June 1, 2010): 741–66. https://doi.org/10.3934/dcds.2010.27.741.Full Text
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Bray, H., S. Brendle, and A. Neves. “Rigidity of area-minimizing two-spheres in three-manifolds.” Communications in Analysis and Geometry 18, no. 4 (January 1, 2010): 821–30. https://doi.org/10.4310/CAG.2010.v18.n4.a6.Full Text
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Bray, H. L., and D. A. Lee. “On the Riemannian Penrose inequality in dimensions less than eight.” Duke Mathematical Journal 148, no. 1 (May 1, 2009): 81–106. https://doi.org/10.1215/00127094-2009-020.Full Text
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Bray, H., and P. Miao. “On the capacity of surfaces in manifolds with nonnegative scalar curvature.” Inventiones Mathematicae 172, no. 3 (June 1, 2008): 459–75. https://doi.org/10.1007/s00222-007-0102-x.Full Text
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Bray, H., S. Hayward, M. Mars, and W. Simon. “Generalized inverse mean curvature flows in spacetime.” Communications in Mathematical Physics 272, no. 1 (May 1, 2007): 119–38. https://doi.org/10.1007/s00220-007-0203-9.Full Text
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Bray, H. L., and A. Neves. “Classification of Prime 3-Manifolds with Yamabe Invariant Greater than RP^3.” Annals of Mathematics 159, no. 1 (January 2004): 407–24.Link to Item
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Bray, H. L. “Black Holes, Geometric Flows, and the Penrose Inequality in General Relativity.” Notices of the American Mathematical Society 49, no. 11 (2002): 1372–81.
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Bray, H. L., and K. Iga. “Superharmonic Functions in R^n and the Penrose Inequality in General Relativity.” Communications in Analysis and Geometry 10, no. 5 (2002): 999–1016.
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Bray, H., and F. Finster. “Curvature estimates and the Positive Mass Theorem.” Communications in Analysis and Geometry 10, no. 2 (January 1, 2002): 291–306. https://doi.org/10.4310/CAG.2002.v10.n2.a3.Full Text
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Bray, H. L. “Proof of the riemannian penrose inequality using the positive mass theorem.” Journal of Differential Geometry 59, no. 2 (January 1, 2001): 177–267. https://doi.org/10.4310/jdg/1090349428.Full Text
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Bray, H., K. McCormick, R. O. Wells, and X. D. Zhou. “Wavelet variations on the Shannon sampling theorem.” Bio Systems 34, no. 1–3 (January 1995): 249–57. https://doi.org/10.1016/0303-2647(94)01457-i.Full Text
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Martinez-Medina, L. A., H. Bray, and T. Mattos. “On wave dark matter in spiral and barred galaxies (Submitted),” n.d.Link to Item
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Book Sections
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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 H. Bray and W. Minicozzi. Beijing and Boston: Higher Education Press and International Press, 2011.Link to Item
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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 H. Bray and W. Minicozzi. Beijing and Boston: Higher Education Press and International Press, 2011.Link to Item
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Bray, H. “The Positve Energy Theorem and Other Inequalities.” In The Encyclopedia of Mathematical Physics, 2005.
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Bray, H. “Geometric Flows and the Penrose Inequality.” In Encyclopedia of Mathematical Physics: Five-Volume Set, 510–20, 2004. https://doi.org/10.1016/B0-12-512666-2/00058-4.Full Text
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Bray, H., 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. Birkhauser, 2004.Link to Item
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Bray, H., and R. M. Schoen. “Recent Proofs of the Riemannian Penrose Conjecture.” In Current Developments in Mathematics, 1–36. Somerville, MA: International Press, 1999.
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Other Articles
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Bray, Hubert, Sven Hirsch, Demetre Kazaras, Marcus Khuri, and Yiyue Zhang. “Spacetime Harmonic Functions and Applications to Mass.” Edited by Mikhail L. Gromov and H Blaine Lawson. Perspectives in Scalar Curvature. World Scientific, February 1, 2023.Link to Item
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Bray, Hubert, and Amir Aazami. “Classification of Preferential Ballot Voting Methods.” Constitutional Political Economy. Springer, n.d.
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Conference Papers
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Bray, H. L., and A. R. Parry. “Modeling wave dark matter in dwarf spheroidal galaxies.” In 9th Biennial Conference on Classical and Quantum Relativistic Dynamics of Particles and Fields (Iard 2014), Vol. 615, 2015. https://doi.org/10.1088/1742-6596/615/1/012001.Full Text Link to Item
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Bray, H. “Black Holes and the Penrose Inequality in General Relativity.” In Proceedings of the International Congress of Mathematicians, 2:257–72, 2002.Link to Item
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Bray, H., and F. Morgan. “An isoperimetric comparison theorem for schwarzschild space and other manifolds.” In Proceedings of the American Mathematical Society, 130:1467–72, 2002. https://doi.org/10.1090/S0002-9939-01-06186-X.Full Text
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Bray, H. “A Family of Quasi-local Mass Functionals with Monotone Flows.” In Proceedings of the 14th International Congress on Mathematical Physics, edited by J. C. Zambrini, n.d.
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Theses and Dissertations
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- Teaching & Mentoring
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Recent Courses
- MATH 491: Independent Study 2023
- ETHICS 89S: Special Topic: First-Year Seminar in Ethics 2022
- MATH 89S: First-Year Seminar 2022
- MATH 323S: Geometry 2022
- MATH 353: Ordinary and Partial Differential Equations 2022
- MATH 421: Differential Geometry 2022
- MATH 491: Independent Study 2022
- MATH 722: Differential Geometry 2022
- MATH 723S: Geometry 2022
- ECON 394: Research Independent Study 2021
- ETHICS 89S: Special Topic: First-Year Seminar in Ethics 2021
- MATH 89S: First-Year Seminar 2021
- MATH 323S: Geometry 2021
- MATH 353: Ordinary and Partial Differential Equations 2021
- MATH 494: Research Independent Study 2021
- MATH 723S: Geometry 2021
- MATH 753: Ordinary and Partial Differential Equations 2021
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Advising & Mentoring
- Professor Bray has supervised 10 Ph.D. graduates (9 in math, 1 in physics) at Duke from 2006 to 2021. He is currently advising 3 Ph.D. candidates in math and 1 Ph.D. candidate in physics.
- Scholarly, Clinical, & Service Activities
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Presentations & Appearances
- Flatly Foliated Relativity: Gravity without Gravitational Waves. Geometry and Relativity Conference. Erwin Schroedinger Institute. August 2017 2017
- From Pythagoras to Einstein: The Geometry of Space and Time. 6th Annual Rockwell Lectures. University of Iowa. March 27, 2017 2017
- The Intersection of Geometry and Physics. 6th Annual Rockwell Lectures. University of Iowa. March 27, 2017 2017
- Geometric Aspects of Special and General Relativity. Invited Address, AMS Southeastern Sectional Meeting. American Mathematical Society. March 12, 2017 2017
- Flatly Foliated Relativity: Gravity without Gravitational Waves. Union College Math Conference, Special Session on Geometric Analysis. December 2, 2016 - December 4, 2016 2016
- Part I: Flatly Foliated Relativity, Part II: The Null Penrose Conjecture. "Geometric Analysis and General Relativity" conference. Banff International Research Station. July 17, 2016 - July 22, 2016 2016
- An Elliptic Theory of Gravity between Special and General Relativity. Research Seminar. Stanford University. May 13, 2016 2016
- Flatly Foliated Relativity: Gravity without Gravitational Waves. Geometry Seminar. University of California, Santa Cruz. May 11, 2016 2016
- On Wave Dark Matter and the Axioms of General Relativity. Colloquium . Mathematics Department, University of California, Santa Cruz. May 10, 2016 2016
- From Pythagoras to Einstein: The Geometry of Space and Time (General audience talk). Faculty of Mathematics Public Lectures : University of Waterloo. March 9, 2015 2015
- The Geometry of the Universe (Research Lecture) : University of Waterloo. March 9, 2015 2015
- The Science behind “Trevor the Time Traveler” (General audience talk). Faculty of Mathematics Public Lectures : University of Waterloo. March 9, 2015 2015
- Two lectures on the geometry of space and time (General audience talks). Faculty of Mathematics Public Lectures : University of Waterloo. March 9, 2015 2015
- The G. Milton Wing Lectures, Lecture 3: "Black Holes and the Monotonicity of the Hawking Mass for Time Flat Surfaces" (Research Style Talk). University of Rochester. April 25, 2014 2014
- The G. Milton Wing Lectures, Lecture 2: "On Dark Matter, Galaxies, and the Large Scale Geometry of the Universe" (Colloquium Style Talk). University of Rochester. April 24, 2014 2014
- The G. Milton Wing Lectures (Series of 3 Lectures, 1 General Public, 1 Colloquium Style, 1 Research Talk). April 23, 2014 - April 25, 2014 2014
- The G. Milton Wing Lectures, Lecture 1: "From Pythagoras to Einstein: The Geometry of Space and Time" (Broad Audience Talk) : University of Rochester. April 23, 2014 2014
- The G. Milton Wing Lectures, Lecture 1: "From Pythagoras to Einstein: The Geometry of Space and Time". October 25, 2013 2013
- The G. Milton Wing Lectures, Lecture 2: "On Dark Matter, Galaxies, and the Large Scale Geometry of the Universe". October 25, 2013 2013
- The G. Milton Wing Lectures, Lecture 3: "Black Holes and the Monotonicity of the Hawking Mass for Time Flat Surfaces". October 25, 2013 2013
- The G. Milton Wing Lectures. October 25, 2013 2013
- On the Monotonicity of the Hawking Mass for Time Flat Surfaces (Research Talk). New York General Relativity Seminar. Columbia University. October 11, 2013 2013
- On Wave Dark Matter and the Geometry of Galaxies (Research Talk). JDG Conference. Lehigh University . May 24, 2013 2013
- On Dark Matter, Galaxies, and the Large Scale Geometry of the Universe (Research Talk). The 20th Southern California Geometric Analysis Seminar. UC-San Diego. February 24, 2013 2013
- On Dark Matter, Spiral Galaxies, and the Axioms of General Relativity (Research Talk). The 41st Barrett Memorial Lectures in Mathematical Relativity. University of Tennessee, Knoxville. May 12, 2011 2011
- On Dark Matter, Spiral Galaxies, and the Axioms of General Relativity (Research Talk). The 26th Annual Geometry Festival. University of Pennsylvania. April 15, 2011 2011
- From Pythagoras to Einstein: How Geometry Describes the Large-Scale Structure of the Universe (Part 1) (Broad Audience Talk). Duke University Graduate Student Recruiting Weekend. Duke University. March 26, 2011 2011
- From Pythagoras to Einstein: How Geometry Describes the Large-Scale Structure of the Universe (Part 2) (Broad Audience Talk). Duke University Graduate Student Recruiting Weekend. Duke University. March 26, 2011 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 2010
- Dark Matter in Galaxies (Dark Matter Awareness Week talk) by Hubert Bray and Andriy Badin (Survey Talk). Dark Matter Awareness Week. Duke University. December 6, 2010 2010
- An Overview of General Relativity (Broad Audience Talk). Duke University Graduate/Faculty Seminar. Duke University. October 3, 2008 2008
- What Do Black Holes and Soap Bubbles Have in Common? (Broad Audience Talk). Duke University Graduate/Faculty Seminar. Duke University. September 21, 2007 2007
- Black Holes and the Curvature of Spacetime (Broad Audience Talk). Michigan State University. November 7, 2005 2005
- Negative Point Mass Singularities in General Relativity (Research Talk). Sir Isaac Newton Institute, Cambridge, England. August 2005 2005
- Black Holes, the Penrose Conjecture, and Quasi-local Mass (Research Talk). 50 Years of the Cauchy Problem in General Relativity. Cargese Summer School - Cargese, Corsica, France. August 2002 2002
- Generalization of the Hawking Mass (Research Talk). 50 Years of the Cauchy Problem in General Relativity. Cargese Summer School - Cargese, Corsica, France. August 2002 2002
- Proof of the Poincare Conjecture for 3-Manifolds with Yamabe Invariant Greater than RP^3 (Research Talk). 50 Years of the Cauchy Problem in General Relativity. Cargese Summer School - Cargese, Corsica, France. August 2002 2002
- Black Holes, Minimal Surfaces, and Geometric Flows (Research Talk). Duke Math Journal Conference. Duke University. April 28, 2001 2001
- Quasi-local Mass and Black Holes in General Relativity (Research Talk) : Duke University . Geometry Seminar. April 28, 2001 2001
- Proof of the Riemannian Penrose Conjecture (Research Talk). Institute for Theoretical Physics - UC Santa Barbara. June 25, 1999 1999
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Outreach & Engaged Scholarship
- Presenter to Harrison Do's 6th Grade Science Classes. Magellan Charter School. November 14, 2016 2016
- Presenter to Harrison Do's 6th Grade Science Classes. Magellan Charter School. November 3, 2015 2015
- Presenter to Harrison Do's 6th Grade Science Classes. Magellan Charter School. March 6, 2015 2015
- Math and Science Tutor, Organizer of Mathletes Program. Emily K Center. 2011 - 2016 2011 - 2016
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Service to the Profession
- Organizer (with Otis Chodosh, Greg Galloway, and Pengzi Miao). Special Session in "Geometric Analysis and General Relativity" . American Mathematical Society. March 10, 2017 - March 12, 2017 2017
- Organizer (with Andrew Cooper). AMS Special Session on Geometric Analysis. American Mathematical Society. November 8, 2014 - November 9, 2014 2014
- Organizer (with Greg Galloway, Rafe Mazzeo, and Natasa Sesum). Park City Mathematics Institute Summer Program on Geometric Analysis. June 30, 2013 - July 20, 2013 2013
- Organizer (with Mark Stern, Lenny Ng, Carla Cederbaum, Luca DiCerbo, and Chris Cornwell). 27th Annual Geometry Festival. April 27, 2012 - April 29, 2012 2012
- Organizer and Presenter at Duke University (along with Andriy Badin). Dark Matter Awareness Week. December 6, 2010 2010
- Organizer (with Benoit Charbonneau, Dick Hain, and Patrick Eberlein). 23rd Annual Geometry Festival held at Duke University. April 25, 2008 - April 27, 2008 2008
- Organizer (with Richard Schoen and Jim Isenberg). AIM / Stanford Relativity Workshop. 2002 2002
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